# A study of center and chiral symmetry realization in thermal $\mathcal{N}=1$ super Yang-Mills theory using the gradient flow

## TL;DR

This paper investigates the realization of center and chiral symmetries in thermal $ ext{SYM}$ using lattice Monte Carlo methods and gradient flow, providing new insights into phase transitions and condensate measurements.

## Contribution

It introduces the use of gradient flow to study symmetry realization and condensates in $ ext{SYM}$, and compares finite temperature phase transitions with superstring theory predictions.

## Key findings

- Deconfinement and chiral restoration occur at similar temperatures.
- Gradient flow enables estimation of condensates at zero temperature.
- Results support conjectures from superstring theory.

## Abstract

The realization of center and chiral symmetries in $\mathcal{N}=1$ super Yang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice by means of Monte Carlo methods. At zero temperature this theory is expected to confine external fundamental charges and to have a non-vanishing gaugino condensate, which breaks the non-anomalous Z$_{2\textrm{N}_{c}}$ chiral symmetry. In previous studies at finite temperatures, the phase transitions corresponding to deconfinement and chiral restoration were observed to occur at roughly the same critical temperature for SU(2) gauge group. We find further evidences for this observation from new measurements at smaller lattice spacings using the fermion gradient flow, and we discuss the agreement of our findings with conjectures from superstring theory. The implementation of the gradient flow technique allows us also to estimate, for the first time, the condensate at zero temperatures and zero gaugino mass with Wilson fermions.