We present new results from our lattice investigations of maximally supersymmetric Yang--Mills theory in three dimensions, focusing on its nonperturbative phase diagram. Using a lattice formulation that preserves part of the supersymmetry algebra at finite lattice spacing, we study the spatial deconfinement transition, which holography relates to the transition between localized and homogeneous black branes in the dual gravity theory. Our analysis employs $N_L^2 \times N_T$ lattices with $N = 8$ colors in the SU($N$) gauge group, considering $N_T = 8$, $10$ and $12$, in each case with aspect ratios $\alpha = N_L/N_T \leq 3$. The resulting transition temperatures are consistent with the holographic low-temperature, large-$N$ prediction $T_c \propto \alpha^3$, providing further evidence for the gauge--gravity correspondence in this setting.

We introduce the formulation of domain wall fermions in the context of lattice QCD. We prove the recovery of exact chiral symmetry in the limit of an infinite fifth direction, and derive the effective four-dimensional operator satisfying the Ginsparg-Wilson relation obtained in this limit. We discuss the residual breaking of chiral symmetry for finite extent of the fifth direction, and how it is affected by spectral features of the Wilson kernel. We also discuss various improvements of domain wall fermions including notably Möbius fermions. These notes are a chapter contributed to the on-line book ``Lattice QCD at 50 years'' (LQCD@50).

External electromagnetic fields provide a useful probe of QCD matter, but real electric fields are hindered by the sign problem, motivating studies with imaginary electric fields. We investigate mesonic screening correlators in lattice QCD at finite temperature in the presence of such a background using staggered fermions. At low temperature, scalar screening masses increase with the field strength, while pseudo-scalar masses remain largely unchanged, and charge-asymmetric channels show additional structure. At high temperature, the correlators exhibit clear spatial oscillations with frequencies set by the quark electric charges. These results demonstrate nontrivial modifications of screening properties induced by external electric fields.

Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavor universality. Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic $B_s\to D_s^*\ell\nu_\ell$ decays using the narrow width approximation. Our data are based on RBC/UKQCD's set of 2+1 flavor gauge field ensembles with Shamir domain-wall fermion and Iwasaki gauge field action featuring inverse lattice spacings of $a^{-1}=$1.785, 2.383, and 2.785 GeV as well as pion masses between 268 and 433 MeV. Light, strange and charm quarks are simulated using domain-wall fermions, whereas bottom quarks are generated with the relativistic heavy quark (RHQ) action.

We demonstrate the use of the gradient flow combined with the short flow-time expansion (GF+SFTX) as a renormalization procedure for four-quark operator matrix elements and associated bag parameters relevant to neutral heavy-meson mixing ($\Delta Q=2$) and heavy-meson lifetimes ($\Delta Q=0$). Using six RBC/UKQCD 2+1-flavor domain-wall fermion ensembles, we calculate for a charm-strange system with physical quark masses flowed bag parameters and match them to the $\overline{\text{MS}}$ scheme using perturbative SFTX coefficients up to next-to-next-to-leading order in QCD. We employ a multi-scale matching strategy and a renormalization-group improved flow-time evolution which allows for a reliable estimate of systematic uncertainties. For a fictitious neutral $D_s$ meson, we obtain the $\Delta Q=2$ $\overline{\text{MS}}$ bag parameter ${\cal B}^{\overline{\text{MS}}}_1(3\,{\rm GeV})=0.7673(123)$, consistent with existing short-distance $D^0$ mixing determinations. For the $\Delta Q=0$ lifetime-ratio operator basis, we find the $\overline{\text{MS}}$ results $B^{\overline{\text{MS}}}_1(3\,{\rm GeV})=1.0524(97)$, $B^{\overline{\text{MS}}}_2(3\,{\rm GeV})=0.9621(71)$, $\epsilon^{\overline{\text{MS}}}_1(3\,{\rm GeV})=-0.2275(76)$, and $\epsilon^{\overline{\text{MS}}}_2(3\,{\rm GeV})=-0.0005(8)$. We provide conversion formulae to re-express these results for an arbitrary choice of evanescent operators. These results demonstrate that GF+SFTX can deliver precise determinations of dimension-six four-quark operators and establish a framework for future lattice computations including more complex operator bases, where the challenge of power-divergent mixing is shifted to the continuum and handled in the SFTX.

Hadron structure calculations using lattice Quantum Chromodynamics (QCD) have advanced significantly in recent years. Results for charges, form factors, and lower Mellin moments can be obtained to high precision, generalized parton distributions can now be computed either directly or reconstructed from moments, and transverse-momentum-dependent distributions can be accessed through direct lattice calculations. Together, these quantities provide detailed and complementary insights into the internal structure of hadrons. These theoretical developments are highly relevant to the experimental program of the Electron-Ion Collider (EIC) and of other facilities. We review the most pertinent lattice QCD results for hadron structure that inform the EIC scientific agenda, with particular emphasis on the pion, kaon, and nucleon.

The numerical sign problem remains one of the central challenges in computational physics. The Worldvolume Hybrid Monte Carlo (WV-HMC) method has recently been proposed as a reliable and computationally efficient algorithm that crucially avoids the ergodicity issues inherent in Lefschetz-thimble approaches. In these proceedings, after outlining the key ideas behind WV-HMC, we present its extension to group manifolds. This provides a rigorous framework for applying WV-HMC to lattice gauge theories.

We present a protocol for actively suppressing Gauss law violations in quantum simulations of SU(2) lattice gauge theory. The protocol uses mid-circuit measurements to extract a characterization of the gauge-violation sector at each lattice vertex, resolving both the total angular momentum and magnetic quantum numbers of the violation via a group quantum Fourier transform. Syndrome-conditional recovery operations map the state back to the gauge-invariant subspace through an iterative sweep over vertices, a procedure we call gauge cooling. We show that while the Knill-Laflamme conditions are not generically satisfied at vertices with nontrivial singlet multiplicity, every single-qubit error is detected by the gauge syndrome. We demonstrate gauge cooling on a single-plaquette simulation of the Kogut-Susskind Hamiltonian truncated to the spin-$1/2$ representation under depolarizing and amplitude damping noise, showing that the protocol restores gauge invariance and improves fidelity at noise rates representative of current superconducting hardware.

AI agents powered by large language models exhibit strong reasoning and problem-solving capabilities, enabling them to assist scientific research tasks such as formula derivation and code generation. However, whether these agents can reliably perform end-to-end reproduction from real scientific papers remains an open question. We introduce PRBench, a benchmark of 30 expert-curated tasks spanning 11 subfields of physics. Each task requires an agent to comprehend the methodology of a published paper, implement the corresponding algorithms from scratch, and produce quantitative results matching the original publication. Agents are provided only with the task instruction and paper content, and operate in a sandboxed execution environment. All tasks are contributed by domain experts from over 20 research groups at the School of Physics, Peking University, each grounded in a real published paper and validated through end-to-end reproduction with verified ground-truth results and detailed scoring rubrics. Using an agentified assessment pipeline, we evaluate a set of coding agents on PRBench and analyze their capabilities across key dimensions of scientific reasoning and execution. The best-performing agent, OpenAI Codex powered by GPT-5.3-Codex, achieves a mean overall score of 34%. All agents exhibit a zero end-to-end callback success rate, with particularly poor performance in data accuracy and code correctness. We further identify systematic failure modes, including errors in formula implementation, inability to debug numerical simulations, and fabrication of output data. Overall, PRBench provides a rigorous benchmark for evaluating progress toward autonomous scientific research.

We present a comprehensive theoretical investigation of the magnetic moments of open heavy-flavor molecular pentaquarks with quark compositions $b\bar{c}qqq$ and $c\bar{b}qqq$ (where $q=u,d,s$). Employing a molecular picture in which the pentaquarks are treated as S-wave bound states of a heavy baryon and a meson, we systematically construct the complete spin--flavor wavefunctions for the two distinct SU(3)$_f$ octet representations, $8_{1f}$ and $8_{2f}$, arising from symmetric and antisymmetric light-diquark configurations, respectively. Within the framework of the constituent quark model, we calculate the magnetic moments of spin-parity configurations, $J^P = \frac{1}{2}^-(\frac{1}{2}^+\otimes 0^-)$ and $J^P = \frac{1}{2}^-, \frac{3}{2}^-(\frac{1}{2}^+\otimes 1^-)$, for each member of the $b\bar{c}$ and $c\bar{b}$ octets. Our results reveal a striking hierarchy: in the $8_{2f}$ representation, the $\frac{1}{2}^+\otimes 0^-$ states exhibit near-universal magnetic moments ($\mu \approx -0.062\,\mu_N$ for $b\bar{c}qqq$ and $\mu \approx +0.362\,\mu_N$ for $c\bar{b}qqq$), as a direct consequence of the spin-singlet light-diquark that suppresses light-quark contributions. In contrast, the $8_{1f}$ representation shows a broad spectrum of values with frequent sign changes, reflecting the active role of the symmetric light-diquark. The clear differences between the $b\bar{c}$ and $c\bar{b}$ families demonstrate explicit heavy-quark flavor symmetry breaking in electromagnetic observables. These predictions provide a detailed set of electromagnetic benchmarks that can serve as discriminants for the internal flavor structure and spin configuration of future experimentally observed open heavy-flavor pentaquarks, offering valuable guidance for ongoing and future searches at facilities such as LHCb and Belle II.

We calculate the dimension-six $\Delta Q=0$ four-quark matrix elements describing heavy-meson lifetime ratios using the gradient flow with its short flow-time expansion as a renormalization procedure. On six RBC/UKQCD 2+1-flavor domain-wall fermion ensembles, we determine flowed bag parameters for physical charm and strange quarks and match to the $\overline{\text{MS}}$ scheme with perturbative short flow-time expansion coefficients through next-to-next-to-leading order (NNLO). A multi-scale matching procedure using renormalization-group running improves the extrapolation to zero flow time. For the operators relevant to $\tau(D_s)/\tau(D^0)$ at the SU(3)$_{\rm F}$ symmetric point, we obtain $B_1^{\overline{\text{MS}}}(3\,{\rm GeV})=1.0524(97)$,$B_2^{\overline{\text{MS}}}(3\,{\rm GeV})=0.9621(70)$, $\epsilon_1^{\overline{\text{MS}}}(3\,{\rm GeV})=-0.2275(76)$, and $\epsilon_2^{\overline{\text{MS}}}(3\,{\rm GeV})=-0.0005(8)$ using a specific choice of evanescent operators. This is the first lattice-QCD determination of $\Delta Q=0$ four-quark operators with a full error budget. It opens the path towards higher-precision predictions of heavy-meson lifetimes and similar quantities exhibiting operator mixing under renormalization.

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based approaches while maintaining low computational costs. In this paper, as a general framework for applying WV-HMC to lattice gauge theories, we extend the algorithm to systems defined on compact group manifolds. The key is to introduce a symplectic structure on the tangent bundle of the worldvolume and formulate molecular dynamics upon it. The validity of the proposed algorithm is demonstrated using the one-site model with a purely imaginary coupling constant.

We propose a new and simple method for determining the renormalized quark masses from lattice simulations. Renormalized quark masses are an important input to many phenomenological applications, including searching and modeling physics beyond the Standard Model. The non-perturbative renormalization is performed using gradient flow combined with the short-flow-time expansion that is improved by renormalization-group (RG) running to match to the $\overline{\text{MS}}$-scheme. Implementing the RG running perturbatively, we demonstrate this method works reliably at least up to the charm-quark mass and exhibits an easily-attainable ``windowing condition''. Using RBC/UKQCD's (2+1)-flavor Shamir domain-wall fermion ensembles with Iwasaki gauge action, we find $m_s^\overline{\text{MS}}(\mu=2 \text{ GeV}) = 90(3)$ MeV and $m_c^\overline{\text{MS}}(\mu=3 \text{ GeV}) = 972(16)$ MeV. These results predict the scale-independent ratio $m_c/m_s= 12.1(4)$. Generalization to other observables is possible, providing an efficient approach to determine non-perturbatively renormalized fermionic observables like form factors or bag parameters from lattice simulations.

We present a lattice-QCD calculation of the hadronic form factors for $B$-meson semileptonic decays computed using the highly improved staggered quark action for both valence and sea quarks on the MILC collaborations 2+1+1-flavor ensembles with lattice spacing ranging from 0.09 fm to 0.03 fm, many with physical pion masses On our finest ensembles, we compute the form factors directly at the physical $b$-quark mass. We discuss the computational setup and analysis strategies for two- and three-point correlation functions. For $B_{(s)} \to D_{(s)}$ we present preliminary results of chiral-continuum fits for the scalar and vector form factors. The goal of this project is a percent-level determination of the scalar and vector form factors to enable high-precision determinations of $|V_{ub}|$ and $|V_{cb}|$. This work fits into a broader program of lattice-QCD studies of weak $B$-meson decays by the Fermilab Lattice and MILC Collaborations.

We study conserved charges of the staggered fermion Hamiltonian in 3+1 dimensions. By decomposing staggered fermions into Majorana components and exploiting lattice translation symmetries, we construct a set of conserved non-singlet charges. We analyze their algebra andshow that, although the charges exhibit nontrivial non-commutativity on the lattice, they generate axial SU(2)_L \tines SU(2)_R transformations for low-energy degrees of freedom in the continuum limit. Possible implications for anomalies are discussed.

The encoding of lattice gauge theories onto quantum computers requires a discretization of the gauge field's Hilbert space on each link, which presents errors with respect to the Kogut--Susskind limit. In the electric basis, Hilbert space fragmentation has recently been shown to limit the excitation of large electric fields. Here, we leverage this to develop a formalism for estimating the size of truncation errors in the electric basis. Generically, the truncation error falls off as a factorial of the field truncation. Examples of this formalism are applied to the Schwinger model and a pure U(1) lattice gauge theory. For reasonable choices of parameters, we improve on previous error estimates by a factor of 10^{306}.