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Aspects of four-point functions in N = 4 SYM at strong coupling

Aspects of four-point functions in N = 4 SYM at strong coupling
Aspects of four-point functions in N = 4 SYM at strong coupling
In this thesis we focus on two main topics: the double-trace spectrum of strongly-coupled N = 4 SYM theory and the construction of one-loop four-point functions in AdS5×S 5 . We begin by providing a basic review of N = 4 SYM and its connection to holographic correlators on AdS5×S 5 through the AdS/CFT duality. In the second part, we examine the spectrum of double-trace operators at strong coupling, which are dual to two-particle bound states in AdS. At large N, these states are degenerate and to obtain their order 1/N2 anomalous dimensions one has to solve a mixing problem. We present a compact formula for all tree-level supergravity anomalous dimensions and we observe an interesting pattern of residual degeneracies. Considering further string corrections, we identify a ten-dimensional principle which dictates the structure of the string corrected spectrum. The third part is devoted to the construction of one-loop corrections to four-point correlation functions. We develop an algorithm for bootstrapping one-loop supergravity correlators for arbitrary Kaluza-Klein modes, which relies solely on implementing the consistency of the OPE to order 1/N4 . We illustrate the subtle features of this algorithm by constructing new explicit results for multi-channel correlators. Lastly, we consider one-loop string corrections to the <O_2O_2O_2O_2> correlator. We find that a transcendental weight three function involving a new type of singularity is required, whose presence is a novelty in the context of AdS amplitudes.
University of Southampton
Paul, Hynek
4f7ce88c-6890-4341-a126-f5a53329be63
Paul, Hynek
4f7ce88c-6890-4341-a126-f5a53329be63
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db

Paul, Hynek (2020) Aspects of four-point functions in N = 4 SYM at strong coupling. University of Southampton, Doctoral Thesis, 178pp.

Record type: Thesis (Doctoral)

Abstract

In this thesis we focus on two main topics: the double-trace spectrum of strongly-coupled N = 4 SYM theory and the construction of one-loop four-point functions in AdS5×S 5 . We begin by providing a basic review of N = 4 SYM and its connection to holographic correlators on AdS5×S 5 through the AdS/CFT duality. In the second part, we examine the spectrum of double-trace operators at strong coupling, which are dual to two-particle bound states in AdS. At large N, these states are degenerate and to obtain their order 1/N2 anomalous dimensions one has to solve a mixing problem. We present a compact formula for all tree-level supergravity anomalous dimensions and we observe an interesting pattern of residual degeneracies. Considering further string corrections, we identify a ten-dimensional principle which dictates the structure of the string corrected spectrum. The third part is devoted to the construction of one-loop corrections to four-point correlation functions. We develop an algorithm for bootstrapping one-loop supergravity correlators for arbitrary Kaluza-Klein modes, which relies solely on implementing the consistency of the OPE to order 1/N4 . We illustrate the subtle features of this algorithm by constructing new explicit results for multi-channel correlators. Lastly, we consider one-loop string corrections to the <O_2O_2O_2O_2> correlator. We find that a transcendental weight three function involving a new type of singularity is required, whose presence is a novelty in the context of AdS amplitudes.

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Published date: November 2020

Identifiers

Local EPrints ID: 447282
URI: http://eprints.soton.ac.uk/id/eprint/447282
PURE UUID: c6ec8abb-cb80-4841-aed7-4252910604dd
ORCID for Hynek Paul: ORCID iD orcid.org/0000-0002-2202-7971

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Date deposited: 08 Mar 2021 17:32
Last modified: 22 Apr 2021 01:49

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