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arXiv · 1601.04670

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

Valentina Forini·Lorenzo Bianchi·Marco S. Bianchi·Björn Leder·Edoardo Vescovi
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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}.

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Valentina Forini, Lorenzo Bianchi, Marco S. Bianchi, Björn Leder, Edoardo Vescovi. 2016-01-18. Lattice and string worldsheet in AdS/CFT: a numerical study. https://arxiv.org/abs/1601.04670

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