Non-relativistic CFT and Semi-classical Strings

TL;DR

This paper explores non-relativistic 3D CFTs via gravity duals in type IIB string theory, analyzing semi-classical strings to understand operator dimensions and energy loss mechanisms for particles.

Contribution

It provides a detailed analysis of semi-classical string solutions in non-relativistic backgrounds, revealing new insights into operator anomalous dimensions and energy dissipation behaviors.

Findings

Anomalous dimensions depend on quantum numbers for specific string configurations.

Energy loss for slow particles is exponential with a temperature-dependent timescale.

Fast particles lose energy inversely proportional to time, independent of temperature.

Abstract

We study different features of 3D non-relativistic CFT using gravity description. As the corresponding gravity solution can be embedded into the type IIB string theory, we study semi-classical closed/open strings in this background. In particular we consider folded rotating and circular pulsating closed strings where we find the anomalous dimension of the dual operators as a function of their quantum numbers. We also consider moving open strings in this background which can be used to compute the drag force. In particular we find that for slowly moving particles, the energy is lost exponentially and the characteristic time is given in terms of the temperature, while for fast moving particles the energy loss goes as inverse of the time and the characteristic time is independent of the temperature.