Quantum field theory through a stringy mirror - Integrability of the AdS5xS5 superstring and its deformations

Describing quantum field theories at finite coupling is a daunting open problem in theoretical physics. One particular theory where we are able to gain valuable insight is planar N=4 supersymmetric Yang-Mills theory (SYM), related to superstring theory on AdS5 x S5 through the AdS/CFT correspondence. Thanks to integrable structures in both theories we can compute the energy spectrum of the string exactly, giving us the spectrum of scaling dimensions in N=4 SYM at finite coupling. In this thesis we firstly briefly review the computation of energy spectra in two-dimensional integrable quantum field theories by means of the (mirror) thermodynamic Bethe ansatz and show how this applies to the AdS5 x S5 superstring. We then fully extend these considerations to various integrable deformations of the superstring and its dual N=4 SYM, breaking some or all of the supersymmetry. We also discuss the application of these methods to a particularly complicated type of excited string state with complex momenta. Finally we consider deformations of the integrable structure of the superstring related to Pohlmeyer reduced string theory and find the corresponding thermodynamic Bethe ansatz equations which exhibit remarkable features.