Exploring the Exact Spectrum in Gauge/String Dualities

Student thesis: Doctoral ThesisDoctor of Philosophy


Understanding the dynamics of strongly coupled gauge theories is one of the greatest challenges in modern theoretical physics. A new hope in attacking this problem was brought by the surprising discovery of integrability in a special four-dimensional gauge theory { the N = 4 supersymmetric Yang-Mills theory (SYM) in the limit of large number of colors. Quantum integrability manifests itself as a powerful hidden symmetry which allows to explore the theory far beyond the conventional perturbative regime, and may even lead to its exact solution. Integrability should also shed light on the striking gauge/string duality, which holographically relates N = 4 SYM with a string theory in curved geometry.

In this thesis we focus on one of the key quantities in the N = 4 SYM theory { its spectrum of conformal dimensions, which correspond to string state energies. The study of integrability has culminated in reformulation of the spectral problem as a compact set of Riemann-Hilbert type equations known as the Quantum Spectral Curve (QSC). We demonstrate the power of this framework by applying it to study the spectrum in a wide variety of settings. The new methods which we present allow to explore previously unreachable regimes. We rst discuss an all-loop solution in a near-BPS limit, leading also to new strong coupling predictions. Next we describe an ecient numerical algorithm which allows to compute the nite-coupling spectrum with nearly unlimited precision (e.g. 60 digits in some important cases). We also present a universal analytic iterative method, which in particular allows to solve a longstanding open problem related to the BFKL limit in which N = 4 SYM develops close links with QCD. Finally we propose the extension of the QSC to the deformed case corresponding to a cusped Wilson line, uncovering new algebraic features of the construction. This allows to systematically study the generalized quark-antiquark potential and generate numerous new results.
Date of Award2016
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorNikolay Gromov (Supervisor) & Nadav Drukker (Supervisor)

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