Generating functionals of correlation functions of p-form currents in AdS/CFT correspondence

TL;DR

This paper calculates the generating functional for correlation functions of massless p-form currents in AdS/CFT, deriving boundary-to-bulk Green's functions and confirming known special cases.

Contribution

It constructs boundary-to-bulk Green's functions for p-form potentials and derives the proportional constant of current correlations in AdS/CFT.

Findings

Derived the proportional constant for current correlations.

Constructed boundary-to-bulk Green's functions for p-form potentials.

Confirmed consistency with known special cases.

Abstract

The generating functional of correlation functions of the currents corresponding to general massless $p$-form potential is calculated in $AdS/CFT$ correspondence of Maldacena. For this we construct the boundary-to-bulk Green's functions of $p$-form potentials. The proportional constant of the current-current correlation function, which is related to the central charge of the operator product expansion, is shown to be $c=(d-p\over 2\pi^{d/2}) (\Gamma (d-p) \over \Gamma ({d\over 2}-p)).$ The result agrees with the known cases such as $p=1$ or 2.