Superconvergence and Duality

TL;DR

This paper explores superconvergence relations in gauge theories, demonstrating their connection to the physical state space and phase transitions, and confirms their predictions through duality in SUSY theories.

Contribution

It establishes a link between superconvergence relations and the physical state space, and verifies their predictions in SUSY gauge theories using duality and conformal algebra.

Findings

Superconvergence relations restrict the physical state space.

Phase transition occurs at a specific matter field boundary.

Results agree with duality predictions in SUSY theories.

Abstract

Superconvergence relations for the transverse gauge field propagator can be used in order to show that the corresponding gauge quanta are not elements of the physical state space, as defined by the BRST algebra. With a given gauge group, these relations are valid for a limited region in the number of matter fields, indicating a phase transition at the boundary. In the case of SUSY gauge theories with matter fields in the fundamental representation, the results predicted by superconvergence can be compared directly with those obtained on the basis of duality and the conformal algebra. There is exact agreement.