On non-relativistic $Q\bar Q$ potential via Wilson loop in Galilean space-time

TL;DR

This paper computes the static quark-antiquark potential in a non-relativistic setting using Wilson loops within the gauge/string duality framework, focusing on Galilean-invariant theories and analyzing constraints on dynamical exponents.

Contribution

It introduces a method to derive the $Q\bar Q$ potential in non-relativistic theories with Galilean symmetry via Wilson loops and explores the conditions on the dynamical exponent $z$.

Findings

Derived the $Q\bar Q$ potential in Galilean space-time.

Identified restrictions on the dynamical exponent $z$ for physical potentials.

Analyzed convexity conditions for the potential in non-relativistic theories.

Abstract

We calculate the static Wilson loop from string/gauge correspondence to obtain the $Q\bar Q$ potential in non-relativistic quantum field theory, i.e. CFT with Galilean symmetry. We analyze the convexity conditions \cite{bachas} for $Q\bar Q$ potential in this theory, and obtain restrictions for the acceptable dynamical exponent $z$.