# Lattice and string worldsheet in AdS/CFT: a numerical study

, Bianchi, L., Bianchi, M. S. , Leder, B. & Vescovi, E. (2015). Lattice and string worldsheet in AdS/CFT: a numerical study. PoS(LATTICE 2015), 244..

## Abstract

We consider a possible discretization for the gauge-fixed Green-Schwarz (two-dimensional) sigma-model action for the Type IIB superstring and use it for measuring the cusp anomalous dimension of planar $\mathcal{N}=4$ SYM as derived from string theory. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and a Wilson-like fermion discretization. In this preliminary study, we compare our results with the expected behavior for very large values of $g=\frac{\sqrt{\lambda}}{4\pi}$, which is the perturbative regime of the sigma-model, and find a qualitative agreement at finite lattice spacing. For smaller $g$ the continuum limit is obstructed by a divergence. We also detect a phase in the fermion determinant, whose origin we explain, which for small $g$ leads to a sign problem not treatable via standard reweigthing. Results presented here are discussed thoroughly in~\cite{toappear}.

Publication Type: Article Contribution to the proceedings of Lattice 2015, July 14--18, Kobe, Japan hep-lat; hep-lat; hep-th School of Mathematics, Computer Science & Engineering
 Preview
Text - Published Version