Nonperturbative phase diagram of two-dimensional $\mathcal{N}=(2,2)$ super-Yang--Mills

Abstract

We consider two-dimensional $\mathcal{N}=(2,2)$ Yang--Mills theory with gauge group SU($N$) in Euclidean signature compactified on a torus with thermal fermion boundary conditions imposed on one cycle. We perform non-perturbative lattice analyses of this theory for large $12\le N\le 20$. Although no holographic dual of this theory is yet known, we conduct numerical investigations to check for features similar to the two-dimensional $\mathcal{N}=(8,8)$ Yang--Mills theory, which has a well-defined gravity dual. We perform lattice field theory calculations to determine the phase diagram, observing a spatial deconfinement transition similar to the maximally supersymmetric case. However, the transition does not continue to low temperature, implying the absence of a topology-changing transition between black hole geometries in any holographic dual for this four-supercharge theory.

v2: Added references, no change in results. Version consistent with the journal version. Data release at http://doi.org/10.5281/zenodo.10083864, 15 pages, 5 figures

References in corpus (15)

• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Observing dynamical supersymmetry breaking with euclidean lattice simulations
• Geometry of Orbifolded Supersymmetric Lattice Gauge Theories
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• Euclidean lattice simulation for the dynamical supersymmetry breaking
• N=4 Supersymmetry on a Space-Time Lattice
• Parallel software for lattice N=4 supersymmetric Yang--Mills theory
• First results from simulations of supersymmetric lattices
• Some physics of the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory: Lattice Monte Carlo study
• Two-dimensional N=(2,2) super Yang-Mills theory on computer
• Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory
• Lattice studies of supersymmetric gauge theories
• Anomaly and Sign problem in $\mathcal{N}=(2,2)$ SYM on Polyhedra : Numerical Analysis
• Large-$N$ limit of two-dimensional Yang--Mills theory with four supercharges