Circular strings in Kerr-$AdS_5$ black holes

TL;DR

This paper investigates pulsating string solutions in Kerr-AdS_5 black holes, analyzing their energy spectra and quantum corrections to understand dual gauge theory operators at finite temperature.

Contribution

It introduces new pulsating string solutions in Kerr-AdS_5 and semi-classically quantizes them, providing insights into dual gauge theory anomalous dimensions.

Findings

Derived energy spectra as functions of quantum numbers.

Calculated quantum corrections to string energies.

Interpreted results as dispersion relations near conformal points.

Abstract

The quest for extension of holographic correspondence to the case of finite temperature naturally includes Kerr-AdS black holes and their field theory duals. We probe the five-dimensional Kerr-AdS space time by pulsating strings. First we find particular pulsating string solutions and then semi-classically quantize the theory. For the string with large values of energy, we use the Bohr-Sommerfeld analysis to find the energy of the string as a function of a large quantum number. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which according to the holographic dictionary are related to anomalous dimensions of certain operators in the dual gauge theory. The interpretation of results from holographic point of view is not straightforward since the dual theory is at finite temperature. Nevertheless, near or at conformal point the expressions can be thought of as the dispersion relations of stationary states.