arXane › Physics
Wednesday, 4 November 2026: 3 new papers, 3 cross-lists and 4 replacements in High Energy Physics - Lattice (hep-lat), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
Adding a trace deformation to the Yang-Mills action keeps the theory confining above the standard deconfinement temperature, in the so-called reconfined phase. We study the confining flux tube of the trace-deformed $\mathrm{SU}(2)$ theory in three dimensions with lattice simulations of Polyakov loop correlators. As the deformation increases, the ground state energy departs from the usual Nambu-Got\=o effective string description, and deep in the reconfined phase the data are accurately described by the Polchinski-Yang rigid string, an effective string dominated by an extrinsic-curvature term.
Numerical simulation of field theories with complex actions is frustrated by the sign problem, which causes an exponential growth in statistical sampling noise. A key example of such a theory is QCD at finite baryon chemical potential, which has important applications to the structure of atomic nuclei and neutron stars. Until now, the sign problem has precluded the possibility of first-principles numerical calculations that could provide key insight into these important physical systems. In this work, we propose an approach to avoiding this limitation by applying a reweighting procedure coupled with a multi-level Monte-Carlo sampling algorithm that offers an exponential enhancement of statistics to counteract the sign problem. We test the approach on a simpler model that displays the same sign problem at finite chemical potential. Our results demonstrate the promise of the proposed approach, significantly increasing the range over which precise calculations are possible, and providing improvements all the way up to the phase transition.
Because of the fermion doubling problem, it has been a longstanding challenge to describe a lattice algorithm for studying four-dimensional gauge theories coupled to chiral fermions. Recently, an algorithm to do so has been described by Craig, extending partial results in the previous literature. Here we describe a variant of this algorithm, based on interpolating a lattice gauge field over the continuum (as in Craig's work) and coupling the interpolated gauge field to continuum chiral fermions. The same variant was also proposed recently by Hsu. In any dimension and for any anomaly-free representation, this approach can be implemented on a computer in principle, but not in practice by Monte Carlo methods because the chiral fermion path integral is not positive.
Calorons, i.e., instantons on $\mathbb{R}^3\times S^1$, with nontrivial asymptotic holonomy decompose into $N$ fundamental monopole constituents. This suggests that a doubly-periodic Yang--Mills instanton on $\mathbb{R}^2\times T^2$ may admit a description in terms of a periodic array of monopole constituents. Starting from the Atiyah--Drinfeld--Hitchin--Manin (ADHM) construction, we derive the $2$d Abelian Hitchin system with impurities as a dual description of the doubly-periodic instanton. We then give a prescription for reconstructing the instanton from the Green's function of this system, assuming a scaling ansatz for the ultraviolet divergences induced by the delta-function impurities. In the far-field limit with strongly anisotropic torus periods, we extend the analysis of Bruckmann and van Baal for multi-calorons and identify an alternating chain of BPS and Kaluza--Klein (KK) monopole constituents: The monopole-center vortex chain arises from the non-Abelian self-dual field especially when an 't Hooft twist cuts the torus into the $1/N$ fragment.
We investigate the phase diagram and nature of the phase transitions of three-dimensional compact lattice Abelian Higgs models with negative gauge coupling. These models describe multicomponent complex scalar fields coupled to a compact U(1) gauge field. Negative gauge coupling favors frustrated plaquette configurations, competing with the tendency of the matter ferromagnetic-like interaction to suppress frustration. Monte Carlo simulations and finite-size scaling analyses of models with one- and two-component scalar fields of unit charge reveal a substantially richer phase structure than at nonnegative gauge coupling. For two components, the O(3) transition line associated with gauge-invariant bilinear ordering extends into the negative-coupling region, and turns into a first-order transition line with decreasing $K$, toward the fully-frustrated $K\to -\infty$ limit. An analogous first-order transition line is also found for the one-component scalar matter with negative gauge coupling. Both one- and two-component models exhibit two additional continuous transition lines at sufficiently large matter coupling. Their energy-cumulant scaling is consistent with three-dimensional Ising and XY critical exponents, suggesting topological transitions in the $\mathbb Z_2$ and XY gauge universality classes, respectively. These results uncover additional phases generated by the competition between matter ordering and dynamical gauge frustration, whose physical characterization remains an open question.
We construct an exact map between continuum fermion fields and lattice fields in 1+1 dimensions. This map rewrites a continuum Hamiltonian as a lattice Hamiltonian with nearest-neighbor couplings and an infinite-dimensional local Hilbert space. The resulting lattice model reproduces exactly the energy spectrum, global operator algebra, chiral symmetries, and anomalies of the continuum QFT on any finite lattice. Unlike domain wall fermions, truncating the local Hilbert space introduces no extra massless modes, and the entanglement entropy of an interval converges as the truncation is removed. The lattice local algebras are of type I and lie between the type III continuum algebras of nested spatial regions, in accordance with the split property. We demonstrate this construction explicitly for $N$ Majorana fermions, realizing the $\mathrm{O}(N)_\mathrm{L}\times\mathrm{O}(N)_\mathrm{R}$ lattice chiral symmetry. We also construct an exact lattice model for the Schwinger model and numerically reproduce the mass gap $e/\sqrt{\pi}$.