Holography on the lattice: the string worldsheet perspective

TL;DR

This paper reviews lattice studies of the Green-Schwarz string action in the context of holography, focusing on discretization, numerical methods, and challenges in non-perturbative analysis relevant to N=4 super Yang-Mills theory.

Contribution

It provides a comprehensive overview of lattice approaches to the gauge-fixed string worldsheet, highlighting recent progress and remaining challenges in non-perturbative holographic computations.

Findings

Discretization techniques for the string worldsheet are discussed.

Numerical exploration methods for the gauge-fixed string are reviewed.

Challenges in non-perturbative lattice studies of holographic models are identified.

Abstract

We review the study, on the lattice, of the Green-Schwarz gauge-fixed string action describing worldsheet fluctuations about the minimal surface holographically dual to the null cusp Wilson loop, useful to evaluate the cusp anomaly of N = 4 super Yang-Mills (sYM). We comment on discretization, numerical explorations and challenges for the non-perturbative study of this benchmark model of gauge-fixed worldsheet actions.