Aspects of Spontaneous Symmetry Breaking in the Lightcone Conformal Truncation Method
This event is part of the Preliminary Oral Exam.
The task of obtaining non-perturbative information about the structure of QFTs is known to be a formidable one. In the aforementioned category falls the study of critical points and phase transitions, which is of particular interest in relativistic field theory, because they arise when the system develops long range interactions, and in turn becomes scale invariant. Additionally, many times the starting theory from which the flow to a critical point points is also scale invariant. Recently, a framework that explicitly takes advantage of this structure has been developed, called lightcone conformal truncation (LCT), in essence a computational tool that allows for appropriate truncation of the Hilbert space of the theory, all that while preserving explicit conformal invariance expected to be seen in the beginning and the end of the flow. After a brief introduction to the basic ingredients that go into LCT, a relativistic massive boson in 1+1 dimensions, in a quartic potential with a cubic deformation is studied. Using our computational tool, we outline the phase diagram of this theory and attempt to characterize it, using data from the energy spectrum and correlation functions.