Aspects of quantum integrability and quantum chaos

Abstract

This thesis bundles the doctoral research about aspects of two important branches of high-energy physics: quantum integrability and quantum chaos. These two topics encompass the author’s work [1–8].

First, the part on quantum integrability covers two topics: hexagon formalism and TT deformation [1–3]. The hexagon formalism is a computational technique used to calculate the structure constants from the three-point functions in N=4 super Yang-Mills theory. This technique relies heavily on the integrability of N=4 super Yang-Mills theory and translate it into the language of the spin chains. The study investigates three operators composed of two determinant operators and one trace operator. TTbar deformation refers to a specific irrelevant deformation in two-dimensional quantum field theory. This deformation possesses unique features and exhibits close connections to other research areas such as string theory, holography, and quantum field theory coupled with dilaton gravity. The observations presented in two separate papers [2,3] include: i)issues on the choice of energy-momentum tensor and extra degrees of freedom, ii) an explicit proof of the existence of supersymmetry after the deformation, and iii) the revelation of its coincidence with spontaneously symmetry broken models.

Secondly, the part on quantum chaos delves into the pole-skipping phenomenon [4–8]. Poleskipping points refer to the points in the momentum space which make the Green’s function indeterminate. The investigation initially focused on the energy-momentum tensor two-point function. It was discovered that the positions of the uppermost pole-skipping points are relevant to the Lyapunov exponent and butterfly velocity, which characterize the intensity and the propagation velocity of the chaos. The author’s works [4–8] involve the exploration of the overall structure of pole-skipping points for general integer-spin fields.