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

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 $A_2^{\ast }$ 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.

1+6 pages, proceedings for the 36th International Symposium on Lattice Field Theory (22-28 July 2018). v2 -- Fixed typos and added two references

References in corpus (8)

• Universal hydrodynamics of non-conformal branes
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• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
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Cited by in corpus (2)

• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories