Exact results in gauge theories

• Applicant: Professorin Elli Pomoni, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2015 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 265593201

Significant progress has been achieved in the study of gauge theories in the last decade. Thanks to integrability, localization and the AdS/CFT correspondence, the field now possess a plethora of exact results that previously seemed unreachable. Unfortunately, the majority of these results have been obtained only for the most symmetric and most unrealistic gauge theory in four dimensions, N = 4 super-Yang Mills. To advance this state of the art, our project aims at investigating which methods are transferable to theories with less supersymmetry and at obtaining exact results for more realistic cases. Our first objective is to obtain exact anomalous dimensions for composite operators in purely gluonic sectors that serve as probes of the AdS factor of the dual geometry for gauge theories with N = 2 and N =1 supersymmetry by combining localization and integrability techniques. Finally, we want to explore how much can be achieved in similar purely gluonic sectors in non-supersymmetric theories. Our second objective is to compute anomalous dimensions in sectors with quarks that probe the compact dimensions of the gravity dual for different gauge theories with N = 2 and N = 1 supersymmetry. Our third objective is to use the data produced before in order to collect clues from the gauge theory side (bottom up approach) for the nature of respective gravity duals. Our fourth objective is to establish these gravity duals using string theory and supergravity techniques (top down approach). Our fifth and last objective is to study the connections between exact results in N = 2 gauge theories and 2D CFTs as well as integrable models. The scope is to learn more about N = 2 gauge theories on one side, and 2D CFTs and Integrable models on the other. Exploiting this interplay, we will ultimately search for similar relations between N = 1 gauge theories and 2D CFTs and/or integrable models.

• DFG Programme: Independent Junior Research Groups