RG Cascades in Hyperbolic Quiver Gauge Theories

TL;DR

This paper classifies supersymmetric 4D quantum field theories into ordinary, affine, and indefinite classes, revealing new properties of hyperbolic theories and their roles in string theory, RG flows, and duality cascades.

Contribution

It introduces a comprehensive classification of supersymmetric QFT$_{4}$s, especially exploring the less-studied indefinite class and hyperbolic theories, with realizations in string theory and analysis of RG flows.

Findings

Hyperbolic quiver theories share properties with ordinary and affine classes.

Hyperbolic subset has unique features in type IIB backgrounds with non-zero axion.

RG flows and duality cascades are studied for hyperbolic theories.

Abstract

In this paper, we provide a general classification of supersymmeric QFT$_{4}$s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super QFT$_{4}$s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT$_{4}$s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made.