Abstract
In this work we present a systematic study of ${\mathrm{AdS}}_{d+1}$ loop amplitudes for gluons and gravitons using momentum space techniques. Inspired by the recent progress in tree-level computation, we construct a differential operator that can act on a scalar factor in order to generate gluon and graviton loop integrands: this systematizes the computation for any given loop level Witten diagram. We then give a general prescription in this formalism, and discuss it for bubble, triangle, and box diagrams.
Highlights
The gauge gravity duality or the AdS=conformal field theory (CFT) is the correspondence between weakly coupled theories of gravity in anti–de Sitter space and conformal field theories with large N
We have studied a formalism to compute loop amplitudes in anti–de Sitter space in Fourier space for gauge theory and gravity loops in AdSdþ1
We have constructed a differential operator which can act on a scalar factor to yield both Yang-Mills and gravity loop correlators
Summary
The gauge gravity duality or the AdS=CFT is the correspondence between weakly coupled theories of gravity in anti–de Sitter space and conformal field theories with large N. Work in loop amplitudes is still in a developing stage It was shown in [23,24,25] that higher point gravity and gauge theory tree amplitude takes a simplified form with the judicious use of momentum space formalism. Many of the results in flat space loop calculations have shown the connection between trees and loops [80,81] and gravitational theories to gauge theories [82], and the loop amplitudes correspond to geometric structures [83] Many of these deep connections and powerful mathematical structures have occurred in the context of gauge and gravity theory and with the usage of momentum space.
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