Dissertations, Theses, and Capstone Projects
Date of Degree
9-2025
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy
Program
Physics
Advisor
Sebastian Franco
Committee Members
Alexios Polychronakos
V. Parameswaran Nair
Dimitra Karabali
Daniel Kabat
Subject Categories
Elementary Particles and Fields and String Theory
Keywords
Quantum Field Theory, String Theory, Relevant Deformations, D-branes, Brane Engineering, Brane Brick Models
Abstract
The thesis studies relevant deformations of 2d gauge theories with $\mathcal{N}=(0,2)$ supersymmetry, realized on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. Brane brick models are the primary means for engineering such theories and streamlining their connection to geometry. In this thesis, we relevant deformations of brane brick models, focusing on a specific class of deformations in which the initial and final theories are both described by brane brick models. Relevant deformations serve as an additional, systematic way of generating these theories, as well as uncovering connections between them. Within the framework of brane engineering, these deformations acquire a geometric interpretation, relating not only gauge theories but also the probed CY$_4$s. Because of the interplay between geometry and field theory, the deformations provide us with additional tools that facilitate the study of both.
Chapter 1 sets the stage by reviewing brane brick models. We begin with an overview of 2d $\mathcal{N}=(0,2)$ theories on D1-branes and their connection to geometry. After a quick tour on toric manifolds, we continue with brane brick models. These are type IIA configurations of NS5- and D5-branes, related by T-duality to D1-branes over CY 4-folds. We explain how these brane configurations give rise to field theories and present the tools necessary for their study.
Having familiarized ourselves with the framework of operations, we proceed to study relevant deformations. The simplest case of a relevant deformation is a mass deformation, which is the subject of chapter 2. Utilizing pairs of theories connected by mass deformations, we demonstrate their implementation in the context of 2d $\mathcal{N}=(0,2)$ theories. Furthermore, we explore their impact on the geometry probed by the D1-branes along with the effect they have on global symmetries.
Chapter 3 generalizes the previous results by considering deformations involving higher order couplings. These present us with new challenges, such as the identification of the necessary operators and the determination of their relevancy. A solution to this issue comes from the geometric aspects of the field theories. We demonstrate how the probed CY$_4$ can be used to determine the scaling dimensions of the fields as well as guide us in identifying the necessary operators. The chapter also explores an interplay between relevant deformations and triality, which is an IR equivalence between gauge theories with the same ambient space. Consequently, these can be treated as different phases of the same theory. Triality allows us to map cubic couplings in one phase of the initial theory to mass terms in another, simplifying the identification and implementation of the deformation. Finally, throughout chapters 2 and 3, we study the volume of the base manifold of the CY$_4$ toric cones. By considering its behavior under relevant deformations, we are led to conjecture a relation between that and the degrees of freedom of the gauge theory.
Recommended Citation
Goulas, Georgios P., "Relevant Deformations of Brane Brick Models" (2025). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6440
