Modern techniques for solvable models

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

In this thesis we study boundary integrable systems associated with the AdS/CFT duality. We focus on N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. Integrable boundary conditions are introduced by studying observables involving Maldacena-Wilson lines.
Firstly, we study a cusped Maldacena-Wilson line with scalar insertions at the cusp, in a simplifying limit called the ladders limit. We provide a rigorous proof of the integrability of this observable. This is done by making a first-principles derivation of the holographic dual of the observable — which takes the form of an integrable open spin-chain (fishchain). Furthermore, we derive a Baxter equation which can be solved to obtain the non-perturbative spectrum of scal-ing dimensions of any number of scalar insertions at the cusp.
Then, we move on to study the one-dimensional defect CFT that lives on the infinite straight 1/2-BPS Maldacena-Wilson line in N = 4 SYM. Operator insertions on the Wilson line are mapped to cor-relation functions in the defect CFT. In order to study the spectrum of operator insertions on the line, we describe it using the quantum spectral curve (QSC) approach. The QSC is then used to derive a Baxter equation which allows us to access the non-perturbative spectrum of an infinite subsector of the defect CFT.
Finally, by combining our results using integrability techniques with the conformal bootstrap we are able to obtain precise non-perturbative values of the structure constant of a three-point function in the defect CFT, for a wide range of the ‘t Hooft coupling. This is the first result of this kind for a nontrivial correlation function involving short operators, for which no other calculational methods have been found so far.
Date of Award1 Nov 2021
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorNikolay Gromov (Supervisor) & Andrea Cavaglia (Supervisor)

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