Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces

TL;DR

This paper classifies five-dimensional supersymmetric gauge theories, exploring their consistency conditions, fixed points, and connections to Calabi-Yau geometries, revealing new insights into singularities and dualities in string theory.

Contribution

It provides a comprehensive classification of 5D supersymmetric gauge theories with nontrivial fixed points and links these theories to Calabi-Yau space degenerations.

Findings

Identified all gauge groups and matter content with fixed points.

Connected gauge theory fixed points to Calabi-Yau singularities.

Classified a new class of Calabi-Yau singularities.

Abstract

We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of nontrivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with nontrivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the ``del Pezzo contractions'' and occur at higher codimension walls of the K\"{a}hler cone.