### Wormholes from two-sided $T \bar{T}$-deformation

We introduce a new coupling between stress tensors of the CFTs living on the two boundaries of the BTZ black hole. Similar to the $T \bar{T}$-deformation, the system exhibits universal properties and is solvable. The resulting geometry is an extreme case of a wormhole with the right and left BTZ wedges glued together along the horizons. We show that the geometry is realized by uniform shock waves emanating from both asymptotic boundaries. The construction has profound implications for the structure of the Hilbert space of states of the dual QFT.

### Classical Soft Theorem in the AdS-Schwarzschild spacetime in small cosmological constant limit

We have studied scattering of a probe particle by a four dimensional AdS-Schwarzschild black hole at large impact factor. Our analysis is consistent perturbatively to leading order in the AdS radius and black hole mass parameter. Next we define a proper "soft limit" of the radiation and extract out the "soft factor" from it. We find the correction to the well known flat space Classical Soft graviton theorem due to the presence of an AdS background.

### Interacting Conformal Carrollian Theories: Cues from Electrodynamics

We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics, which surprisingly, is not obtainable as an ultra-relativistic limit of Maxwellian Electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self consistent algorithm working hand in hand with imposing invariance under infinite dimensional Conformal Carroll algebra (CCA). It requires inclusion of new fields in the dynamics and the system in free of gauge redundancies. We calculate two-point functions in the free theory based entirely on symmetry principles. We next add interaction (quartic) terms to the free Lagrangian, strictly constrained by conformal invariance and Carrollian symmetry. Finally, a successful dynamical realization of infinite dimensional CCA is presented at the level of charges, for the interacting theory. In conclusion, we calculate the Poisson brackets for these charges.

### Quantum field theory with dynamical boundary conditions and the Casimir effect II: Coherent states

We have previously studied -in part I- the quantization of a mixed bulk-boundary system describing the coupled dynamics between a bulk quantum field confined to a spacetime with finite space slice and with timelike boundary, and a boundary observable defined on the boundary. Our bulk system is a quantum field in a spacetime with timelike boundary and a dynamical boundary condition -the boundary observable's equation of motion. Owing to important physical motivations, in part I, we have computed the renormalized local state polarization and local Casimir energy for both the bulk quantum field and the boundary observable in the ground state and in a Gibbs state at finite, positive temperature. In this work, we introduce an appropriate notion of coherent and thermal coherent states for this mixed bulk-boundary system, and extend our previous study of the renormalized local state polarization and local Casimir energy to coherent and thermal coherent states.

### Constructing Canonical Feynman Integrals with Intersection Theory

Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct $d\log$-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals, and project them into master integrals using intersection theory. This provides a constructive way to build canonical master integrals whose differential equations can be solved easily. We use our method to investigate both the maximally cut integrals and the uncut ones at one and two loops, and demonstrate its applicability in problems with multiple scales.

### Single Level String Theory

The $\mathbf{O}(D,D)$ covariant generalized metric, postulated as a truly fundamental variable, can describe novel geometries where the notion of Riemannian metric ceases to exist. Here we quantize a closed string upon such backgrounds and identify flat, anomaly-free, non-Riemannian string vacua in the familiar critical dimension, $D{=26}$ (or $D{=10}$). Remarkably, the whole BRST closed string spectrum is restricted to just one level with no tachyon, and matches the linearized equations of motion of Double Field Theory. Taken as an internal space, our non-Riemannian vacua may open up novel avenues alternative to traditional string compactification.

### Sphere partition function of Calabi-Yau GLSMs

The sphere partition function of Calabi-Yau gauged linear sigma models (GLSMs) has been shown to compute the exact Kaehler potential of the Kaehler moduli space of a Calabi-Yau. We propose a universal expression for the sphere partition function evaluated in hybrid phases of Calabi-Yau GLSMs that are fibrations of Landau-Ginzburg orbifolds over some base manifold. Special cases include Calabi-Yau complete intersections in toric ambient spaces and Landau-Ginzburg orbifolds. The key ingredients that enter the expression are Givental's I/J-functions, the Gamma class and further data associated to the hybrid model. We test the proposal for one- and two-parameter abelian GLSMs, making connections, where possible, to known results from mirror symmetry and FJRW theory.

### Dressed Dirac Propagator from a Locally Supersymmetric ${\cal N}=1$ Spinning Particle

We study the Dirac propagator dressed by an arbitrary number $N$ of photons by means of a worldline approach, which makes use of a supersymmetric ${\cal N} = 1$ spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator.

### On the Lorentz-invariance of the Dyson series in theories with derivative couplings

We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $\phi ^4$ theory. We eventually give evidence that Lorentz invariance is satisfied and that usual Feynman rules can be applied to the interaction Lagrangian.

### Crossing versus locking: Bit threads and continuum multiflows

Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu-Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. We investigate for which choices of bound a given set of boundary regions can be "locked", in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.

### Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS$_4$ Black Holes

We numerically study the topologically twisted index of several three-dimensional supersymmetric field theories on a genus $g$ Riemann surface times a circle, $\Sigma_g\times S^1$. We show that for a large class of theories with leading term of the order $N^{3/2}$, where $N$ is generically the rank of the gauge group, there is a universal logarithmic correction of the form $\frac{g-1}{2} \log N$. We explain how this logarithmic subleading correction can be obtained as a one-loop effect on the dual supergravity theory for magnetically charged, asymptotically AdS$_4\times M^7$ black holes for a large class of Sasaki-Einstein manifolds, $M^7$. The matching of the logarithmic correction relies on a generic cohomological property of $M^7$ and it is independent of the black hole charges. We argue that our supergravity results apply also to rotating, electrically charged asymptotically AdS$_4\times M^7$ black holes. We present explicitly the quiver gauge theories and the gravity side corresponding to $M^7=N^{0,1,0}, V^{5,2}$ and $Q^{1,1,1}$.

### The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further we demonstrate an equivalent formalism of computation using a general time independent Hamiltonian having well defined eigenstate representation for integrable supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism we consider the two well known models viz. Harmonic Oscillator and one dimensional potential well within the framework of supersymmetry. For the Harmonic Oscillator case we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without supersymmetry. On the other hand, for one dimensional potential well problem we found significantly different time scale and the other parameter dependence compared to the results obtained from non-supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model independent Hamiltonian along with the previously mentioned these well cited models.

### Electrodynamics of Thin Sheets of Twisted Material

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity", which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic waves with wavelength larger than the thickness of the sheet. We show that the low-frequency Faraday rotation angle has different behaviors in different phases. For an insulator, the Faraday angle behaves as $\omega^2$ at low frequencies, with the coefficient being determined by the linear relationship between a component of the electric quadrupole moment and the external electric field. For superconductors, the Faraday rotation angle is constant when the frequency of the incoming EM waves is below the superconducting gap and is determined by the coefficient of the Lifshitz invariant in the Ginzburg-Landau functional describing the superconducting state. In the metallic state, we show that the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. The theory is general and is applicable to strongly correlated phases.

### Lattice simulations of a gauge theory with mixed adjoint-fundamental matter

In this article we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge theories with mixed representation fields have been suggested to describe the fundamental interactions well beyond the electroweak unification scale, and they are also closely related to supersymmetric QCD. In addition, they are studied as deformations of theories with pure adjoint matter in the context of adiabatic continuity. We provide some first results for bare parameter tuning and interdependence of the two representations. We also investigate how the chiral symmetry breaking or a conformal scenario can be realized and checked in such theories.

### Ramsey interferometry as a witness of acceleration radiation

We adapt a typical Ramsey interferometer by inserting a linear accelerator capable of accelerating an atom inside a single-mode cavity. We demonstrate that this simple scheme allows us to estimate the effects of acceleration radiation via interferometric visibility. By using a Rydberg-like atom, our results suggest that, for the transition regime of the order of GHz and interaction time of 1 ns, acceleration radiation effects can be observable for accelerations as low as $10^{17}$ m/s$^2$.

### Computing cohomology intersection numbers of GKZ hypergeometric systems

In this review article, we report on some recent advances on the computational aspects of cohomology intersection numbers of GKZ systems developed in \cite{GM}, \cite{MH}, \cite{MT} and \cite{MT2}. We also discuss the relation between intersection theory and evaluation of an integral of a product of powers of absolute values of polynomials.

### Fractal Structures of Yang-Mills Fields and Non Extensive Statistics: applications to High Energy Physics

In this work we provide an overview of the recent investigations on the non extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the LHC, hadron physics and neutron stars. We review some recent investigations on the power-law distributions arising in HEP experiments focusing on a thermodynamic description of the system formed, behaviour. The possible connections with a fractal structure of hadrons is also discussed. The main objective of the present work is to delineate the state-of-the-art of those studies, and show some open issues that deserve more careful investigation. We propose several possibilities to test the theory through analyses of experimental data.