New linearization and reweighting for simulations of string sigma-model on the lattice

TL;DR

This paper introduces a new lattice discretization approach for simulating Type IIB string worldsheets, addressing sign problems and analyzing fermionic and bosonic correlators with implications for lattice string theory.

Contribution

It presents a novel linearization and reweighting method to mitigate sign issues in lattice simulations of string sigma-models, including a detailed analysis of fermionic spectra and correlators.

Findings

Sign problem becomes severe with zero eigenvalues of fermionic operator

Reweighting with Pfaffian absolute value allows observable measurement

Observed divergence in fermionic correlators linked to U(1) symmetry breaking

Abstract

We study the discretized worldsheet of Type IIB strings in the Gubser-Klebanov-Polyakov background in a new setup, which eliminates a complex phase previously detected in the fermionic determinant. A sign ambiguity remains, which a study of the fermionic spectrum shows to be related to Yukawa-like terms, including those present in the original Lagrangian before the linearization standard in a lattice QFT approach. Monte Carlo simulations are performed in a large region of the parameter space, where the sign problem starts becoming severe and instabilities appear due to the zero eigenvalues of the fermionic operator. To face these problems, simulations are conducted using the absolute value of a fermionic Pfaffian obtained introducing a small twisted-mass term, acting as an infrared regulator, into the action. The sign of the Pfaffian and the low modes of the quadratic fermionic operator are then taken into account by a reweighting procedure of which we discuss the impact on the measurement of the observables. In this setup we study bosonic and fermionic correlators and observe a divergence in the latter, which we argue - also via a one-loop analysis in lattice perturbation theory - to originate from the U(1)-breaking of our Wilson-like discretization for the fermionic sector.