Bipartite Field Theories from D-Branes

TL;DR

This paper introduces methods using dimer models and mirror symmetry to derive gauge theories from D-brane configurations on toric Calabi-Yau manifolds, including complex D7-brane embeddings, leading to a broad class of Bipartite Field Theories.

Contribution

It develops new tools for constructing Bipartite Field Theories from D-brane setups, especially handling general D7-brane embeddings via recombination.

Findings

Constructed explicit examples of Bipartite Field Theories.

Engineered infinite families of models with planar and non-planar graphs.

Demonstrated the use of mirror symmetry in gauge theory derivation.

Abstract

We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.