Castellano, Ruiz, and Valenzuela recently observed a remarkable "pattern" in infinite-distance limits of moduli spaces in quantum gravity, which relates the field space variation of the mass of the lightest tower of particles to the field space variation of the species scale. In this work, we show how a version of this pattern can be proven to hold for BPS particles and strings throughout the vector multiplet moduli space of a 5d supergravity theory, even in regions where the particle masses and string tensions are substantially modified relative to their asymptotic behavior in the infinite-distance limits. This suggests that a suitably defined version of the pattern may hold not merely in the asymptotic limits of moduli space, but in the interior as well.

We set up a numerical S-matrix bootstrap problem to rigorously constrain bound state couplings given by the residues of poles in elastic amplitudes. We extract upper bounds on these couplings that follow purely from unitarity, crossing symmetry, and the Roy equations within their proven domain of validity. First we consider amplitudes with a single spin 0 or spin 2 bound state, both with or without a self-coupling. Subsequently we investigate amplitudes with the spectrum of bound states corresponding to the estimated glueball masses of pure SU(3) Yang-Mills. In the latter case the 'glue-hedron', the space of allowed couplings, provides a first-principles constraint for future lattice estimates.

Bubbles of nothing (BoNs) describe the decay of spacetimes with compact dimensions and are thus of fundamental importance for many higher dimensional theories proposed beyond the Standard Model. BoNs admit a 4-dimensional description in terms of a singular Coleman-de Luccia (CdL) instanton involving the size modulus field, stabilized by some potential $V(\phi)$. Using the so-called tunneling potential ($V_t$) approach, we study which types of BoNs are possible and for which potentials $V(\phi)$ can they be present. We identify four different types of BoN, characterized by different asymptotic behaviours at the BoN core and corresponding to different classes of higher dimensional theories, which we also classify. Combining numerous analytical and numerical examples, we study the interplay of BoN decays with other standard decay channels, identify the possible types of quenching of BoN decays and show how BoNs for flux compactifications can also be described in 4 dimensions by a multifield $V_t$. The use of the $V_t$ approach greatly aids our analyses and offers a very simple picture of BoNs which are treated in the same language as any other standard vacuum decays.

We show that a class of $L$-loop conformal ladder graphs correspond to twisted partition functions of free massive complex scalars in $d=2L+1$ dimensions. The graphs arise as four-point functions in certain two- and four-dimensional conformal fishnet models. The twisted thermal two-point function of the scalars is a generator of such conformal graphs for all loops. We argue that this correspondence is seeded by a system of two decoupled harmonic oscillators twisted by an imaginary chemical potential. We find a number of algebraic and differential relations among the conformal graphs which mirror the underlying free dynamics.

This work aims to investigate the classical-level duality between the $SIM(1)$-Maxwell-Chern-Simons (MCS) model and its self-dual counterpart. Initially, our focus is on free-field cases to establish equivalence through two distinct approaches: comparing the equations of motion and utilizing the master Lagrangian method. In both instances, the classical correspondence between the self-dual field and the MCS dual field undergoes modifications due to very special relativity (VSR). Specifically, duality is established only when the associated VSR-mass parameters are the same. Furthermore, we analyze the duality when the self-dual model is minimally coupled to fermions. As a result, we show that Thirring-like interactions, corrected for non-local VSR contributions, are included in the MCS model. Additionally, we demonstrate the equivalence of the fermion sectors in both models, thereby concluding the proof of classical-level duality.

We study to what extent, and in what form, the notion of gauge-string duality may persist at finite $N$. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in $\mathrm{AdS}_5 \times S^5$ are holographically dual to certain auxiliary ghosts that compensate for finite $N$ trace relations in $U(N)$ $\mathcal{N}=4$ super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of $U(N)$ $\mathcal{N}=4$ SYM at finite $N$. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing 't Hooft coupling $\lambda = 0$. We propose that a complex, which furnishes a BRST-like resolution of the finite $N$ Hilbert space of a boundary $U(N)$ gauge theory at $\lambda = 0$, should be identified as the space of states of the dual string theory in the $\alpha' \to \infty$ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution.

The Schur index of the Higgs branch of four-dimensional $\mathcal{N}=2$ SCFTs is related to the spectrum of non-unitary two-dimensional CFTs. The rank one case has been shown to lead to the non-unitary CFTs with Deligne-Cvitanovic (DC) exceptional sequence of Lie groups. We show that a subsequence $(A_0, A_{\frac{1}{2}}, A_1, A_2, D_4)$ within the non-unitary sequence is related to a subsequence in the Mathur-Mukhi-Sen (MMS) sequence of unitary theories. We show that 2D non-unitary $G_2$ theory is related to unitary $E_6$ theory, and using this result along with the Galois conjugation, we propose that the $G_2$ Higgs branch is a sub-branch of the $E_6$ Higgs branch.

Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli space of Riemann surfaces. Generalizing previous work, we employ this to study moduli spaces of higher genus surfaces, surfaces with boundaries, and surfaces with cone points. In each case, the knowledge of classical conformal blocks provides an extremely efficient approximation to the Weil-Petersson metric on moduli space. We find detailed agreement with analytic results for volumes and geodesic lengths on moduli space.

The group $SO(d+1,1)$ makes an appearance both as the conformal group of Euclidean space in $d$ dimensions and as the isometry group of de Sitter spacetime in $d+1$ dimensions. While this common feature can be taken as a hint towards holography on de Sitter space, understanding the representation theory has importance for cosmological applications where de Sitter spacetime is relevant. Among the categories of $SO(d+1,1)$ unitary irreducible representations, discrete series is important in physical applications because they are expected to capture gauge fields. However, they are also the most difficult ones to recognize in field theoretical examples compared to representations from the other categories. Here we point towards some examples where we are able to recognize discrete series representations from fields on de Sitter and highlight some of the properties of these representations.

This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results include a study, and finding an application to the higher genus problem, of infinite Coxeter symmetries in the sets of Gopakumar-Vafa invariants; provision of a new class of solutions to the supersymmetric flux vacuum equations which have elsewhere been conjectured to give weight-two modular manifolds; provision of two new conjectural examples of weight-four modular varieties (rank-two attractors); and discussion of a set of numerical relations between infinite sums of Gromov-Witten invariants and critical L-values.

We study the on-shell scattering amplitudes in quantum gravity for high-energy collisions in the eikonal approximation. We first evaluate the $n$-loop 2-particle scattering amplitude in the high energy and low momentum transfer limit. We do so in a symmetrized manner by finding the contributions of each of the particle worldines to the scattering amplitude and gluing them together via the $n$ intermediate particle exchanges. In this limit on applying the eikonal approximation and summing over all $n$-loop Feynman diagrams we obtain a closed form for the 2 particle scattering amplitude. Finally, we extend this approach to obtain a generalized eikonal approximation for $N$-particle scattering at high energies and small momentum transfers. The generalised form of the scattering amplitude can then be used to evaluate the bound states of the system.

Quantum teleportation can be used to define a notion of parallel transport which characterizes the entanglement structure of a quantum state \cite{Czech:2018kvg}. This suggests one can formulate a gauge theory of entanglement. In \cite{Wong:2022mnv}, it was explained that measurement based quantum computation in one dimension can be understood in term of such a gauge theory (MBQC). In this work, we give an alternative formulation of this "entanglement gauge theory" as an extended topological field theory. This formulation gives a alternative perspective on the relation between the circuit model and MBQC. In addition, it provides an interpretation of MBQC in terms of the extended Hilbert space construction in gauge theories, in which the entanglement edge modes play the role of the logical qubit.

We study the structure of wave functions in complex Chern-Simons theory on the complement of a hyperbolic knot, emphasizing the similarities with the topological string/spectral theory correspondence. We first conjecture a hidden integrality structure in the holomorphic blocks and show that this structure guarantees the cancellation of potential singularities in the full non-perturbative wave function at rational values of the coupling constant. We then develop various techniques to determine the wave function at such rational points. Finally, we illustrate our conjectures and obtain explicit results in the examples of the figure-eight and the three-twist knots. In the case of the figure-eight knot, we also perform a direct evaluation of the state integral in the rational case and observe that the resulting wave function has the features of the ground state for a quantum mirror curve.

Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle virtualities. The latter serve as regulators of infrared divergences, thus making these observables finite in four space-time dimensions. In this paper, we use the method of canonical differential equations for calculation of (non)planar double box integrals in the near mass-shell kinematical regime, i.e., where virtualities of external particles are much smaller than the Mandelstam variables involved. We deduce a basis of master integrals with uniform transcendental weight based on the analysis of leading singularities by means of the Baikov representation as well as an array of complementary techniques. We dub the former asymptotically canonical since it is valid in the near mass-shell limit of interest. We iteratively solve resulting differential equations up to weight four in terms of multiple polylogarithms.

We investigate the twist-3 generalized parton distributions (GPDs) for the valence quarks of the proton within the basis light-front quantization (BLFQ) framework. We first solve for the mass spectra and light-front waved functions (LFWFs) in the leading Fock sector using an effective Hamiltonian. Using the LFWFs we then calculate the twist-3 GPDs via the overlap representation. By taking the forward limit, we also get the twist-3 parton distribution functions (PDFs), and discuss their properties. Our prediction for the twist-3 scalar PDF agrees well with the CLAS experimental extractions.

The following is a master thesis centered around the concept of localisation and the Third Way Theory. This thesis discusses various aspects of supersymmetric localisation in one and three dimensions, and contains original results with regards to the Third Way Theory. It starts off with the Witten index for a one-dimensional supersymmetric system and derives various aspects through localisation. After this, the thesis moves on to the Third Way Theory. First, it offers a review of the Third Way Theory, a deformation of topologically massive Yang-Mills theory in three dimensions. Then it moves on to original results. These include a supersymmetrisation of the Third Way Theory and consequently a localisation of the Third Way Theory, which is to say, a method of deriving non-perturbative results.

Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $\Delta(X) = X\otimes X$, then their generating functions obey bilinear Hirota equations and hence are named $\tau$-functions. However, dealing with group elements is not always easy, especially for non-commutative algebras of functions, and this slows down the development of $\tau$-function theory and the study of integrability properties of non-perturbative functional integrals. A simple way out is to use arbitrary elements of the universal enveloping algebra, and not just the group elements. Then the Hirota equations appear to interrelate a whole system of generating functions, which one may call $\textit{generalized}$ $\tau$-functions. It was recently demonstrated that this idea can be applicable even to a somewhat sophisticated case of the quantum toroidal algebra. We consider a number of simpler examples, including ordinary and quantum groups, to explain how the method works and what kind of solutions one can obtain.

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero.

Loop Vertex Expansion (LVE) was developed for the construction of QFT models with local and non-local interactions. Using LVE, one can prove the analyticity in the finite cardioid-like domain in the complex plain of the coupling constant of the free energies and cumulants of various vector, matrix, or tensor-type models. Here, applying the idea of choosing the initial approximation depending on the coupling constant, we construct the analytic continuation of the free energy of the quartic matrix model beyond the standard LVE cardioid over the branch cut and for arbitrary large couplings.

Phase transitions are part of everyday life, yet are also believed to be part of the history of our universe, where the nature of particle interactions change as the universe settles into its vacuum state. The discovery of the Higgs, and measurement of its mass suggests that our vacuum may not be entirely stable, and that a further phase transition could take place. This article is based on a talk in the Oldenberg Series, and reviews how we find the probability of these phase transitions, discussing past work on how black holes can dramatically change the result! Apart from a brief update at the end, this article mostly follows the content of the talk.

We determine the adiabatic tidal contributions to the radiation reacted momentum impulse $\Delta p_i^\mu$ and scattering angle $\theta$ between two scattered massive bodies (neutron stars) at next-to-next-to-leading post-Minkowskian (PM) order. The state-of-the-art three-loop (4PM) worldline quantum field theory toolkit using dimensional regularization is employed to establish the classical observables. We encounter divergent terms in the gravito-electric and gravito-magnetic quadrupolar sectors necessitating the addition of post-adiabatic counterterms in this classical theory. This leads us to include also the leading post-adiabatic tidal contributions to the observables. The resulting renormalization group flow of the associated post-adiabatic Love numbers is established and shown to agree with a recent gravito-electric third post-Newtonian analysis in the non-relativistic limit.

Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a reducible but indecomposable representation of the Carroll group. We also build action principles for all Carroll fermions we introduce; in particular, in even dimensions we provide an action principle for a minimal magnetic Carroll fermion, having the same number of components as a Dirac spinor. We then explore the coupling of these fermions to magnetic Carroll gravity in both its first-order and second-order formulations.

This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an R-matrix of non-difference form. This method has the advantage of being more feasible than directly solving the Yang-Baxter equation. We applied this approach to various contexts, in particular, in the realm of open quantum systems, we achieved the first classification of integrable Lindbladians. These operators describe the dynamics of physical systems in contact with a Markovian environment. Within this classification, we discovered a novel deformation of the Hubbard model spanning three sites of the spin chain. Additionally, we applied our method to classify models with $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$ symmetry and we recovered the matrix part of the S-matrix of $AdS_5 \times S^5$ derived by requiring centrally extended $\mathfrak{su}(2|2)$ symmetry. Furthermore, we focus on spin 1/2 chain on models of 8-Vertex type and we showed that the models of this class satisfy the free fermion condition. This enables us to express the transfer matrix associated to some of the models in a diagonal form, simplifying the computation of the eigenvalues and eigenvectors. The thesis is based on the works: 2003.04332, 2010.11231, 2011.08217, 2101.08279, 2207.14193, 2301.01612, 2305.01922.

We study the phenomenology of superheavy decaying dark matter with mass around $10^{10}$ GeV which can arise in the low-energy limit of string compactifications. Generic features of string theory setups (such as high scale supersymmetry breaking and epochs of early matter domination driven by string moduli) can accommodate superheavy dark matter with the correct relic abundance. In addition, stringy instantons induce tiny $R$-parity violating couplings which make dark matter unstable with a lifetime well above the age of the Universe. Adopting a model-independent approach, we compute the flux and spectrum of high-energy gamma rays and neutrinos from three-body decays of superheavy dark matter and constrain its mass-lifetime plane with current observations and future experiments. We show that these bounds have only a mild dependence on the exact nature of neutralino dark matter and its decay channels. Applying these constraints to an explicit string model sets an upper bound of ${\cal O}(0.1)$ on the string coupling, ensuring that the effective field theory is in the perturbative regime.

We construct and analyze a model of neutron star in the $\kappa$-deformed space-time. This is done by first deriving $\kappa$-deformed generalization of the Einstein tensor, starting from the non-commutative generalization of the metric tensor. By generalising the energy-momentum tensor to the non-commutative space-time and exploiting the $\kappa$-deformed dispersion relation, we then set up Einstein's field equations in the $\kappa$-deformed space-time. As we adopt a realisation of the non-commutative coordinates in terms of the commutative coordinates and their derivatives, our model is constructed in terms of commutative variables. Now by treating the interior of the star to be a perfect fluid as in the commutative space-time, we investigate the modification to neutron star's mass due to non-commutativity of the space-time. We show that the non-commutativity of the space-time enhances the mass limit of the neutron star. Using recent observational limit on the upper bound on the mass of neutron stars, we find the deformation parameter to be $|a|\sim 10^{-44}m$.

We propose a method to compute the effective potential of QCD from gap equations by introducing the homotopy transformation between solutions of the equation of motion. Via this method, the effective potential can be obtained beyond the bare vertex approximation, which then generalizes the Cornwall, Jackiw and Tomboulis (CJT) effective potential for bilocal composite operators. Moreover, the extended effective potential is set to be a function of self energy instead of the composite operator, which is the key point to make the potential bounded from below as for the auxiliary field (AF) Potential. We then apply the effective potential in the coexistence region where there exists at least two solutions, for instance, in vacuum with small current quark mass, and the first order phase transition region in finite temperature and chemical potential, which provides the in-medium behavior of the latent heat and false vacuum energy.

The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, as it allows us to study particles with much higher energies and travelling much longer distances than possible in terrestrial experiments, but more progress is needed on several fronts. A thorough appraisal of current strategies and experimental frameworks, regarding quantum gravity phenomenology, is provided here. Our aim is twofold: a description of tentative multimessenger explorations, plus a focus on future detection experiments. As the outlook of the network of researchers that formed through the COST Action CA18108 "Quantum gravity phenomenology in the multi-messenger approach (QG-MM)", in this work we give an overview of the desiderata that future theoretical frameworks, observational facilities, and data-sharing policies should satisfy in order to advance the cause of quantum gravity phenomenology.

This article is devoted to investigate the effects of $f(R)$ theory in the dynamics of a massless particle near the horizon of a static spherically symmetric (SSS) black hole. Deriving the equations of motion within $f(R)$ gravitational theories, novel solutions for charged and neutral black holes are obtained, introducing a dimensional parameter $a$ in $f(R)=R-2a\sqrt{R}$. Departing from General Relativity, these solutions showcase unique properties reliant on the dynamics of Ricci scalar. Analysis shows that chaos manifests within a specific energy range, with $a$ playing a crucial role. The study underscores the general applicability of the spherically symmetric metric, revealing insights into particle dynamics near black hole horizons. Despite an initially integrable nature, the introduction of harmonic perturbation leads to chaos, aligning with the Kolmogorov-Arnold-Moser theory. This research contributes to a nuanced understanding of black hole dynamics, emphasizing the importance of alternative theories of gravity.

The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop quantum contributions in their most general form. We examine the metric horizons and the nature of the hypersurfaces having constant radius; furthermore, a possible energy-extraction process which violates the null energy condition is described, and both timelike and null geodesics are studied. Our analysis shows that there is no choice of the sign of the constant parameter embodying the quantum correction to the metric which leaves all the features of the classical Schwarzschild solution almost unaffected.

We present an evaluation of the glueball spectrum for configurations produced with $N_f=1$ dynamical fermions as a function of the $m_{\rm PCAC}$ mass. We obtained masses of states that fall into the irreducible representations of the octahedral group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$. Due to the low signal to noise ratio, practically, we can only extract masses for the irreducible representations $R^{PC}=$ $A_1^{++}$, $E^{++}$, $T_2^{++}$ as well as $A_1^{-+}$. We make use of the Generalized Eigenvalue Problem (GEVP) with an operator basis consisting only of gluonic operators. Throughout this work we are aiming towards the identification of the effects of light dynamical quarks on the glueball spectrum and how this compares to the statistically more precise spectrum of SU(3) pure gauge theory. We used large gauge ensembles which consist of ${\sim {~\cal O}}(10 {\rm K})$ configurations. Our findings demonstrate that the low-lying spectrum of the scalar, tensor as well as pseudo-scalar glueballs receive negligible contributions from the inclusion of $N_f=1$ dynamical fermions.

In the perturbative treatment of interacting quantum field theories, if the interaction Lagrangian changes adiabatically in a finite interval of time, secular growths may appear in the truncated perturbative series also when the interaction Lagrangian density is returned to be constant. If this happens, the perturbative approach does not furnish reliable results in the evaluation of scattering amplitudes or expectation values. In this paper we show that these effects can be avoided for adiabatically switched-on interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. We start considering equilibrium background states and show that, when thermalisation occurs (interaction Lagrangian of spatial compact support), secular effects are avoided. Furthermore, no secular effects pop up if the limit where the Lagrangian is supported everywhere in space is taken after thermalisation (large time limit), in contrast to the reversed order. This result is generalized showing that if the interaction Lagrangian is spatially compact, secular growths are avoided for generic background states which are only invariant under time translation and to states whose explicit dependence of time is not too strong. Finally, as an example, we apply the presented theorems to study a complex scalar and a Dirac field in a classical external electromagnetic potential, on a background KMS state, to manifest that a spatially compact supported interaction does not give rise to secular growths.

We find all polynomial tau-functions of the n-th reduced BKP hierarchy (=n-th Sawada-Kotera hierarchy). The name comes from the fact that for n=3 the simplest equation of the hierarchy is the famous Sawada-Kotera equation.

As the study of three-hadron physics from lattice QCD matures, it is necessary to develop proper analysis tools in order to reliably study a variety of phenomena, including resonance spectroscopy and nuclear structure. Reconstructing the three-particle scattering amplitude requires solving integral equations, which can be written in terms of data-constrained dynamical functions and physical on-shell quantities. The driving term in these equations is the so-called one-particle exchange, which leads to a kinematic divergence for particles on-mass-shell. A vital component in defining three-particle amplitudes with definite parity and total angular momentum, which are used in spectroscopic studies, is to project the one-particle exchange into definite partial waves. We present a general procedure to construct exact analytic partial wave projections of the one-particle exchange contribution for any system composed of three spinless hadrons. Our result allows one full control over the analytic structure of the projection, which we explore for some low-lying partial waves with applications to three pions.

Dissipation is a ubiquitous phenomenon in nature that affects the fate of chaotic quantum dynamics. To characterize the interplay between quantum chaos and dissipation in generic quantum many-body systems, we consider a minimal dissipative Floquet many-body system. We study the dissipative form factor (DFF), an extension of the spectral form factor to open quantum systems, of the random phase model in the presence of arbitrary one-site nonunitary gates (quantum channels). In the limit of large local Hilbert space dimension, we obtain an exact expression for the DFF averaged over the random unitary gates, with simple, closed-form expressions in the limit of large times. We find that, for long enough times, the system always relaxes (i.e., the DFF decays) with two distinctive regimes characterized by the presence or absence of gap closing. While the system can sustain a robust ramp for a long (but finite) time interval in the gap-closing regime, relaxation is ``assisted'' by quantum chaos in the regime where the gap remains nonzero. In the latter regime, we find that, if the thermodynamic limit is taken first, the gap does not close even in the dissipationless limit.

We investigate the thermodynamic geometry of the quark-meson model at finite temperature, $T$, and quark number chemical potential, $\mu$. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization group approach. We use recent developments to recast the flow equation into the form of an advection-diffusion equation. We adopt the local potential approximation for the effective average action. We focus on the thermodynamic curvature, $R$, in the $(\mu,T)$ plane, in proximity of the chiral crossover, up to the critical point of the phase diagram. We find that the inclusion of fluctuations results in a smoother behavior of $R$ near the chiral crossover. Moreover, for small $\mu$, $R$ remains negative, signaling the fact that bosonic fluctuations reduce the capability of the system to completely overcome the fermionic statistical repulsion of the quarks. We investigate in more detail the small $\mu$ region by analyzing a system in which we artificially lower the pion mass, thus approaching the chiral limit in which the crossover is actually a second order phase transition. On the other hand, as $\mu$ is increased and the critical point is approached, we find that $R$ is enhanced and a sign change occurs, in agreement with mean field studies. Hence, we completely support the picture that $R$ is sensitive to a crossover and a phase transition, and provides information about the effective behavior of the system at the phase transition.

We show that vacuum type N Kundt spacetimes in an arbitrary dimension admit a Kerr-Schild (KS) double copy. This is mostly done in a coordinate-independent way using the higher-dimensional Newman-Penrose formalism. We also discuss two kinds of non-uniqueness of an electromagnetic field corresponding to a given KS metric (i.e., its single copy) - these originate, respectively, from the rescaling freedom in the KS vector and from the non-uniqueness of the splitting of the KS metric in the flat part and the KS part. In connection to this, we show that the subset of KS pp-waves admits both null and non-null electromagnetic single copies. Since vacuum type N Kundt spacetimes are universal solutions of virtually any higher-order gravities and null fields in such backgrounds are immune to higher-order electromagnetic corrections, the KS-Kundt double copy demonstrated in the present paper also applies to large classes of modified theories.