Quantum Fluctuation on the Worldsheet of Probe String in BTZ Black Hole

In this paper, the authors investigate the second-order normal quantum fluctuation on the worldsheet of a probe string in the Bañados–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, the authors study the correlation function of the Schrödinger functional of excited fields on the worldsheet and further extract the field's formula. This study could shed light on the potential connection between complexity growth and correlation function.