Scattering amplitudes in Lifshitz spacetime

TL;DR

This paper investigates scattering amplitudes in field theories dual to Lifshitz spacetimes, revealing how IR singularities vary with the dynamical exponent and exploring the spacetime's singularity effects.

Contribution

It extends the holographic computation of scattering amplitudes to Lifshitz backgrounds, analyzing IR singularities and their dependence on the Lifshitz exponent z.

Findings

Stronger IR singularity for z > 1 compared to z=1.

Coefficient of IR singularity vanishes as z approaches 1.

Determined minimal surfaces for cusp Wilson loops in Lifshitz spacetime.

Abstract

We consider the calculation of scattering amplitudes in field theories dual to Lifshitz spacetimes. These amplitudes provide an interesting probe of the IR structure of the field theory; our aim is to use them to explore the observable consequences of the singularity in the spacetime. We assume the amplitudes can be related by T-duality to a Wilson loop, as in the AdS case, and determine the bulk minimal surfaces for the simplest cusp Wilson loop. We use this to determine the leading IR singularity in the amplitude. We find there is a stronger IR singularity for z >1 than for z=1, with a coefficient which vanishes as z goes to 1.