AdS$_3$/CFT Correspondence, Poincar\'{e} Vacuum State and Greybody Factors in BTZ Black Holes

TL;DR

This paper investigates greybody factors of BTZ black holes using 2D CFT within the AdS$_3$/CFT correspondence, clarifying the initial state, normalization, and relations among different black hole dimensions.

Contribution

It demonstrates how to determine the normalization factor of greybody factors from bulk-to-boundary Green functions and explores the role of specific operators in the boundary theory.

Findings

Normalization factor fixed by bulk-to-boundary Green function.

Relation among greybody factors in different dimensions shown.

Two types of operators coupling to scalar field boundary values discussed.

Abstract

The greybody factors in BTZ black holes are evaluated from 2D CFT in the spirit of AdS$_3$/CFT correspondence. The initial state of black holes in the usual calculation of greybody factors by effective CFT is described as Poincar\'{e} vacuum state in 2D CFT. The normalization factor which cannot be fixed in the effective CFT without appealing to string theory is shown to be determined by the normalized bulk-to-boundary Green function. The relation among the greybody factors in different dimensional black holes is exhibited. Two kinds of $(h,{\bar h})=(1,1)$ operators which couple with the boundary value of massless scalar field are discussed.