Thermal phase structure of dimensionally reduced super-Yang--Mills

Abstract

We present our current results from ongoing lattice investigations of the Berenstein-Maldacena-Nastase deformation of maximally supersymmetric Yang-Mills quantum mechanics. We focus on the thermal phase structure of this theory, which depends on both the temperature 𝑇 and the deformation parameter 𝜇, through the dimensionless ratios 𝑇/𝜇 and 𝑔 = 𝜆/𝜇 3 with 𝜆 the 't Hooft coupling. We determine the critical 𝑇/𝜇 of the confinement transition for couplings 𝑔 that span three orders of magnitude, to connect weak-coupling perturbative calculations and large-𝑁 dual supergravity predictions in the strong-coupling limit. Analyzing multiple lattice sizes up to 𝑁 𝜏 = 24 and numbers of colors up to 𝑁 = 16 allows initial checks of the large-𝑁 continuum limit.

Lattice studies of supersymmetric gauge theories

“…This BMN model has been studied numerically by Refs. [35,38,[49][50][51][52][53], with particular focus on its finitetemperature confinement transition. The critical temperature T c of this transition can be predicted both by perturbative calculations in the weak-coupling regime g 1 [63][64][65] as well as by dual supergravity calculations for strong couplings g → ∞ with N → ∞ and T…”

“…Good progress has been made by Refs. [49,51,52], considering different lattice discretizations, numbers of colors N , lattice sizes L, and couplings g that span several orders of magnitude.…”

“…Left: For a fixed 't Hooft coupling λ lat = 0.5, only per-mille-level fluctuations are observed for U(N ) gauge groups with N = 2, 3 and 4, up to the largest accessible volumes. Right: For a fixed 4 4 lattice volume, the U(2) phase fluctuations increase significantly for stronger couplings, which obstructs studies of λ lat 4 with this lattice action limit [34,42,52,84,98,99,107,116,120]. Lowerdimensional systems can also be used as testbeds for different algorithmic approaches, such as the complex Langevin method used to explore spontaneous supersymmetry breaking in Ref.…”