Gauge Theory as a String Theory in The Infinite and Zero Tension Limits

Abstract

We investigate formulations of Yang-Mills theory as a string theory in zero and infinite tension limits. For the infinite tension case, a small Regge slope expansion of open bosonic string scattering amplitudes is performed. The leading order term is precisely the Yang-Mills amplitude plus string corrections. We explore monodromy relations among open string scattering amplitudes and their field theory counterparts. Diagrams regarding to these identities, namely Plahte diagrams, are studied. For the tensionless limit, the Yang-Mills theory is described by electric lines of force which can be interpreted as the theory of strings with contact interactions. Both theories agree with each other at the level of the expectation of Wilson loop. To address a non-Abelian theory, the string model is modified by introducing a scalar field into the worldsheet whose dynamics takes the form of the topological BF action. We further analyse an effective action of the BF theory and its connection to the two-dimensional Yang-Mills theory.