N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories

TL;DR

This paper explores the connections between supersymmetric gauge theories, matrix models, and Calabi-Yau geometries, revealing new relationships through deconstruction and relating string amplitudes to matrix models.

Contribution

It introduces a novel framework linking N=1 supersymmetry, matrix models, and bosonic gauge theories via deconstruction, extending known relations to higher dimensions and complex geometries.

Findings

Relates F-terms to c=1 string amplitudes in Calabi-Yau compactifications.

Shows how deconstruction connects 4+k dimensional theories to lower-dimensional bosonic gauge theories.

Demonstrates the use of matrix models to deconstruct higher-dimensional supersymmetric gauge theories.

Abstract

We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1 non-critical bosonic string theory, and express them in a quiver or, equivalently, super matrix model. Moreover we relate, by deconstruction, the uncompactified c=1 theory to the six-dimensional conformal (2,0) theory. Furthermore, we show how we can use the idea of deconstruction to connect 4+k dimensional supersymmetric gauge theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models. Examples of such bosonic systems include unitary matrix models and gauged matrix quantum mechanics, which deconstruct 5-dimensional supersymmetric gauge theories, and Chern-Simons gauge theories, which deconstruct gauge theories living on branes wrapped over cycles in Calabi-Yau threefolds.