Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance

TL;DR

This paper explores gravity duals for non-relativistic theories with scale invariance, revealing conditions under which conformal invariance is preserved, with applications to Reggeon field theory and quantum finance.

Contribution

It provides explicit gravity solutions for scale-invariant non-relativistic theories, analyzing when conformal invariance is maintained or broken under Galilean symmetry.

Findings

Scale invariant deformations preserve non-relativistic conformal invariance under Galilean symmetry.

Constructed metrics solve Einstein equations with a massive vector field.

Applications to Reggeon field theory and non-linear quantum finance are discussed.

Abstract

We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and non-linear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.