Finite Theories and Marginal Operators on the Brane

TL;DR

This paper constructs large classes of finite N=1 supersymmetric 4D theories using branes in Type IIB string theory, linking their finiteness to brane bending and exploring dualities and marginal operators.

Contribution

It introduces a brane-based method to realize finite supersymmetric theories and analyzes their duality symmetries and marginal operators.

Findings

Finite theories correspond to non-bent branes.

Duality group includes SL(2,Z) for many models.

Existence of larger classes with marginal operators.

Abstract

We show how to use D and NS fivebranes in Type IIB superstring theory to construct large classes of finite N=1 supersymmetric four dimensional field theories. In this construction, the beta functions of the theories are directly related to the bending of branes; in finite theories the branes are not bent, and vice versa. Many of these theories have multiple dimensionless couplings. A group of duality transformations acts on the space of dimensionless couplings; for a large subclass of models, this group always includes an overall $SL(2,\ZZ)$ invariance. In addition, we find even larger classes of theories which, although not finite, also have one or more marginal operators.