The properties of $D1$-branes from lattice super Yang--Mills theory using gauge/gravity duality

TL;DR

This paper investigates the properties of D1-branes in two-dimensional supersymmetric Yang-Mills theory using lattice discretization and gauge/gravity duality, focusing on thermodynamic quantities and viscosity in the strongly coupled regime.

Contribution

It introduces a lattice formulation of 2D SYM preserving some supersymmetry and computes thermodynamic properties using gauge/gravity duality, exploring different lattice geometries.

Findings

Calculated free energy, equation of state, and speed of sound for the strongly coupled plasma.

Discussed the non-vanishing bulk viscosity related to the energy-momentum tensor trace.

Compared lattice results with supergravity predictions for D1-brane dynamics.

Abstract

The two-dimensional supersymmetric Yang-Mills (SYM) theory with sixteen supercharges at large $N$ and strong 't~Hooft coupling is conjectured to be dual to certain supergravity solutions in the decoupling limit. We discretize the gauge theory preserving a subset of supersymmetries on the lattice. Based on the choice of a point in the moduli space for the expansion of the gauge links to target the correct continuum theory, one ends up with different lattice geometries. In our previous work, we explored the free energy and the phase structure on a skewed torus corresponding to $A_{2}^{*}$ lattice geometry. Here, we will consider square lattice and calculate the free energy, equation of state and speed of sound in this strongly coupled supersymmetric plasma. Since there is no shear viscosity in two dimensions, we comment on the expectations for the bulk viscosity from the calculations on the dual supergravity side, which unlike the conformal $\mathcal{N}=4$ SYM case does not vanish and is proportional to the trace of energy-momentum tensor.