A Quantum Spectral Curve approach to the cusped Wilson line and the bi-scalar fishnet theory

Student thesis: Doctoral ThesisDoctor of Philosophy


This thesis contains a collection of results obtained both in the cusped Wilson line and the bi-scalar fishnet theory. We focus primarily on results obtained using the Quantum Spectral Curve (QSC), which was originally formulated for local single-trace operators in N = 4 SYM. However, we show that it can be adapted to capture the spectrum of both operator insertions in the cusped Wilson line and of operators in the bi-scalar fishnet model. Our results are in general non-perturbative.
First, we study the anomalous dimension of a cusped Wilson line with operator in-sertions in the planar limit of N = 4 SYM. In the limit when the line becomes straight we interpret the excited states of the QSC as insertions of scalar operators, which recently were intensively studied in the context of the one-dimensional defect CFT living on the line. We obtain a five-loop perturbative result at weak coupling and the first four orders in the 1/√ λ expansion at strong coupling. Additionally, we find the spectrum numerically in a wide range of the coupling and show that one can transition smoothly between the weak and strong coupling regimes, confirming all previous analytic results.
Second, we study the spectrum of a class of operators in the bi-scalar fishnet theory. We extend a previously available QSC description, allowing us to describe a larger collection of operators. We obtain numerical results at finite coupling, as well as all-loop analytic results in certain cases. In both cases we find agreement with results obtained previously.
Third, we consider a new class of twist operators, which can be defined for any theory with a planar limit. This allows us to introduce spacetime deformations in the bi-scalar fishnet model. We discuss the simplest operators in the resulting theory both from a field theoretic point of view, as well as through their QSC description.
Date of Award1 Mar 2020
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorNikolay Gromov (Supervisor)

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