Quantum fluctuation on the worldsheet of probe string in BTZ black hole

TL;DR

This paper studies quantum fluctuations on a probe string in a BTZ black hole, linking these fluctuations to Hawking radiation and exploring their impact on string action growth and complexity via boundary conformal field theory.

Contribution

It introduces a second-order quantum fluctuation analysis on the string worldsheet in BTZ black holes and connects it to boundary CFT correlation functions and complexity growth.

Findings

Quantum fluctuations modify the string's action growth.

Correlation functions of excited fields are derived from boundary vertex operators.

Potential link between complexity growth and correlation functions is suggested.

Abstract

In this paper, we investigate the second-order normal quantum fluctuation on the world-sheet of a probe string in the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. These fluctuations is treated as the projection of Hawking radiation on the worldsheet and indeed modify the action growth of the string. Then in the string field theory/boundary conformal field theory framework, via the boundary vertex operator we study the correlation function of the Schr\"odinger functional of excited fields on the world-sheet and further extract the field's formula. Our study could shed light on the potential connection between complexity growth and correlation function.