Effective Lagrangian for Non-Abelian Two-Dimensional Topological Field Theory

Abstract

We develop a systematic approach to obtain an effective Lagrangian for 2D non-Abelian topological BF theory. A general expression is presented in a diagrammatic representation containing solely scalar fields. Expressions for the SU(2) and SU(3) effective actions are explicitly stated. In the case of SU(2), we show that the effective action can be interpreted as a winding number. By using the SU(2) effective action, the partition function on a sphere for SU(2) Yang-Mills theory is calculated. Moreover, we generalise the theory to include a source term for the gauge field as well as calculate the vacuum expectation value of the Wilson loop based on the effective theory.

38 pages, 3 figures

References in corpus (4)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• $BF$ gravity
• Delta-function Interactions for the Bosonic and Spinning Strings and the Generation of Abelian Gauge Theory
• QED as the tensionless limit of the spinning string with contact interaction

Cited by in corpus (2)

• Path Integral Quantization of Generalized Stueckelberg Electrodynamics: A Faddeev-Jackiw Approach
• Steps Towards Generalization of Tensionless String Theory with Contact Interactions as Wilson loop of Non-Abelian Yang-Mills Theory