Breaking Symmetries: N = 2 Spin Chains and Conformal Field Theory at Finite Temperature

Abstract

Conformal field theories (CFTs) and supersymmetric field theories constitute special classes of quantum field theories with applications ranging from critical phenomena and confinement to quantum gravity via holography. Their large symmetry groups make them ideal testing grounds for theoretical developments, enabling the use of powerful and elegant methods. Among these, conformal bootstrap and integrability have proven particularly successful.

In this thesis, we take steps toward extending these methods beyond their conventional domains by breaking conformal symmetry through finite temperature effects and reducing supersymmetry via orbifolding. For spin chains arising from N = 2 superconformal field theories obtained by orbifolding N = 4 super Yang–Mills theory in four dimensions, we generalize the coordinate Bethe ansatz by incorporating long-range corrections.

On the conformal bootstrap side, after breaking conformality by placing the CFT on a d-dimensional cylinder, we develop an analytic framework based on dispersion relations. We apply this method to several theories, including large-N CFTs in four dimensions. Furthermore, we combine this analytic approach with existing numerical bootstrap techniques at finite temperature to compute new thermal correlation functions in the three-dimensional Ising CFT.