THERMAL ONE-POINT FUNCTIONS IN BLACK-BRANE ANTI-DE SITTER SPACE

Abstract

In the last two decades, the discovery of the AdS/CFT Correspondence has led to many new results and profound consequences in theoretical physics. Here, we explore one aspect of the AdS/CFT correspondence: one-point functions on the boundary of AdS space at finite temperature. While one-point functions typically vanish when we only consider the leading two-derivative, free action, they become non-zero when we consider higher derivative terms. Here in particular, we consider a Weyl correction to the action and find, as expected, that these one-point functions become nonzero and yield interesting values. We then analyze the OPE of a scalar two-point function on the background of Schwarzschild black-brane \(AdS_{d+1}\). We conclude that both the OPE coefficients and the one-point functions vanish for very-massive operators ( \(\Delta \gg 1\) ) - as expected from field theory considerations in the strong-coupling regime. Finally, we perform a similar analysis in the semiclassical limit and find compelling agreement with the computed field theory result.