Boson-fermion correspondence and holomorphic anomaly equation in 2d Yang-Mills theory on torus

• Published in: The journal of high energy physics Vol. 2021; no. 7; pp. 1 - 13
• Main Author: Huang, Min-xin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2021; Springer Nature B.V; SpringerOpen
• Subjects: 1/N Expansion; Classical and Quantum Gravitation; Deformation; Dependence; Elementary Particles; Energy; Fermions; Field Theories in Lower Dimensions; High energy physics; Mathematical analysis; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Topological Strings; Toruses; Yang-Mills theory; Topological Strings; Field Theories in Lower Dimensions; 1/N Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2021)144

A
bstract
Recently, Okuyama and Sakai proposed a novel holomorphic anomaly equation for the partition function of 2d Yang-Mills theory on a torus, based on an anholomorphic deformation of the propagator in the bosonic formulation. Using the boson-fermion correspondence, we derive the formula for the deformed partition function in fermionic description and give a proof of the holomorphic anomaly equation.