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Lattice Studies of Two-Dimensional Maximally Supersymmetric Yang-Mills Theory for Tests of Gauge-Gravity Duality

Bana Singh Sangtan, Anosh Joseph, David Schaich

Abstract

We present our ongoing work on two-dimensional maximally supersymmetric Yang-Mills (2D MSYM) theory using lattice techniques. The continuum theory is obtained from the dimensional reduction of four-dimensional ${\mathcal N} = 4$ supersymmetric Yang-Mills theory. We construct both the continuum and lattice versions of the 2D MSYM theory. The lattice action preserves a subset of supersymmetries. We extend existing lattice software with new routines to accommodate the additional terms in the lower-dimensional theory. This lattice construction enables us to perform Rational Hybrid Monte Carlo simulations of 2D MSYM and facilitates the exploration of its continuum limit. Our work contributes to the numerical study of maximally supersymmetric gauge theories and supports the ongoing efforts to test gauge-gravity duality and investigate related non-perturbative phenomena.

Lattice Studies of Two-Dimensional Maximally Supersymmetric Yang-Mills Theory for Tests of Gauge-Gravity Duality

Abstract

We present our ongoing work on two-dimensional maximally supersymmetric Yang-Mills (2D MSYM) theory using lattice techniques. The continuum theory is obtained from the dimensional reduction of four-dimensional supersymmetric Yang-Mills theory. We construct both the continuum and lattice versions of the 2D MSYM theory. The lattice action preserves a subset of supersymmetries. We extend existing lattice software with new routines to accommodate the additional terms in the lower-dimensional theory. This lattice construction enables us to perform Rational Hybrid Monte Carlo simulations of 2D MSYM and facilitates the exploration of its continuum limit. Our work contributes to the numerical study of maximally supersymmetric gauge theories and supports the ongoing efforts to test gauge-gravity duality and investigate related non-perturbative phenomena.

Paper Structure

This paper contains 8 sections, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Review of thermal large-$N$ 2D MSYM on a circle
  3. Dual gravity description at low temperature
  4. Summary for SYM on a rectangular torus
  5. Behaviour on a skewed torus
  6. 2D MSYM from dimensional reduction
  7. Lattice discretization
  8. Conclusions and Future Directions

Figures (2)

  • Figure 1: Summary of the expected phase structure for 2D MSYM on a rectangular torus. This figure is adapted from Ref. Catterall:2017lub.
  • Figure 2: Summary of the expected behavior of 2D MSYM on a skewed torus varying $t$ with fixed shape parameters $\alpha$ and $\gamma$. The three plots consider $\alpha \ll 1$ (left), $\alpha \gg 1$ (center) and $\alpha \sim 1$ (right). These figures are taken from Ref. Catterall:2017lub.