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

TL;DR

The paper investigates scale-invariant but potentially non-conformal non-relativistic field theories through gravity duals, constructing Einstein-Proca backgrounds and showing that Galilean invariance tends to preserve NR conformal invariance within the studied class.It analyzes holographic two-point functions and their dependence on dynamical exponent Z and particle-number M, and extends to deformations related to Lifshitz-type backgrounds, yielding explicit correlator structures under various symmetry assumptions.Two primary applications are explored: the IR scaling regime of Reggeon field theory and the emergence of non-linear quantum finance from interacting NR field theories, with holographic insights into propagator structure, tail behavior, and multiple effective volatilities.The work highlights the role of the dynamical (Z) and Hurst (H=1/Z) exponents, discusses unitarity and causality constraints, and points to future directions including string-theoretic embeddings and RG-like evolution of Z in the holographic framework.

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.