Exact Results in Supersymmetric Gauge Theories

Abstract

In this thesis we discuss supersymmetric gauge theories, focusing on exact results achieved using methods of integrability. For the larger portion of the thesis we study the N=4 super Yang-Mills theory in the planar limit, a recurring topic being the Konishi anomalous dimension, which is roughly the analogue for the mass of the proton in quantum chromodynamics. The N=4 supersymmetric Yang-Mills theory is known to be integrable in the planar limit, which opens up a wealth of techniques one can employ in order to find results in this limit valid at any value of the coupling. We begin with perturbation theory where the integrability of the theory first manifests itself. Here we showcase the first exact result, the so-called slope function, which is the linear small spin expansion coefficient of the generalized Konishi anomalous dimension. We then move on to exact results mainly achieved using the novel quantum spectral curve approach, the method allowing one to find scaling dimensions of operators at arbitrary values of the coupling. As an example we find the second coefficient in the small spin expansion after the slope, which we call the curvature function. This allows us to extract non-trivial information about the Konishi operator. Methods of integrability are also applicable to other supersymmetric gauge theories such as ABJM, which in fact shares many similarities with N=4 super Yang-Mills. We briefly review these parallel developments in the last chapter of the thesis.

PhD thesis, 154 pages

References in corpus (24)

• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• The Pomeron and Gauge/String Duality
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Quantum corrections to the string Bethe ansatz
• Wrapping at four loops in N=4 SYM
• On the Singularities of the Magnon S-matrix
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Wrapping interactions at strong coupling -- the giant magnon
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• The Quantum Spectral Curve of the ABJM theory
• Twist-three at five loops, Bethe Ansatz and wrapping
• Wronskian Solution for AdS/CFT Y-system
• Konishi operator at intermediate coupling
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
• Scaling dimensions at small spin in N=4 SYM theory
• Sum rules for higher twist sl(2)operators in N=4 SYM
• Operators in the d=4, N=4 SYM and the AdS/CFT correspondence
• On the one-loop curvature function in the $sl(2)$ sector of $\mathcal{N}=4$ SYM