PIRSA:17020126

Loops in AdS from conformal symmetry

Bissi, A. (2017). Loops in AdS from conformal symmetry. Perimeter Institute. https://pirsa.org/17020126

Bissi, Agnese. Loops in AdS from conformal symmetry. Perimeter Institute, Feb. 21, 2017, https://pirsa.org/17020126 

          @misc{ pirsa_PIRSA:17020126,
            doi = {10.48660/17020126},
            url = {https://pirsa.org/17020126},
            author = {Bissi, Agnese},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Loops in AdS from conformal symmetry},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020126 see, \url{https://pirsa.org}}
          }

Agnese Bissi The Abdus Salam International Centre for Theoretical Physics (ICTP)

DOI 10.48660/17020126
Collection
Talk Type Scientific Series
Subject

Abstract

In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT:  the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. The second approach involves Mellin space. As an example, I’ll show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of \phi^4 theory in AdS, the crossing solution reproduces a previous computation of the one-loop bubble diagram. I will end with a discussion on open problems and new developments.