Abstract
We study D-brane instantons in systems of D3-branes at toric CY 3-fold singularities. The instanton effect can be described as a backreaction modifying the geometry of the mirror configuration, in which the breaking of U(1) symmetries by the instanton translates into the recombination of gauge D-branes, which also directly generates the instanton-induced charged field theory operator. In this paper we describe the D-brane instanton backreaction in terms of a combinatorial operation in the bipartite dimer diagram of the original theory. Interestingly, the resulting theory is a general Bipartite Field Theory (BFT), defined by a bipartite graph tiling a general (possibly higher-genus) Riemann surface. This provides the first string theory realization of such general BFTs. We study the general properties of the resulting theories, including the construction of the higher-dimensional toric diagrams and the interplay between backreaction and Seiberg duality. In cases where the non-perturbative effects relate to complex deformations, we show that the procedure reproduces and explains earlier existing combinatorial recipes. The combinatorial operation and its properties generalize to an operation on the class of general BFTs, even including boundaries, relating BFTs defined on Riemann surfaces of different genus.
Highlights
The present paper combines new results in two interesting areas of D-brane physics: nonperturbative D-brane instantons and the realization of Bipartite Field Theories (BFTs) using D-branes.D-brane instantons have become a centerpiece in the understanding of string theory beyond perturbation theory and in model building applications to moduli stabilization or the generation of charged field theory operators
In this paper we show that the resulting gauge theory can be encoded in a Bipartite Field Theory, albeit in general not defined on a 2-torus but on a general Riemann surface, of the kind introduced in [21]
We show that the description of the instanton backreaction can be carried out directly on the dimer diagram, and that it generically turns it into a general BFT
Summary
The present paper combines new results in two interesting areas of D-brane physics: nonperturbative D-brane instantons and the realization of Bipartite Field Theories (BFTs) using D-branes. In this paper we show that the resulting gauge theory (and the charged field theory operators) can be encoded in a Bipartite Field Theory, albeit in general not defined on a 2-torus (as the original dimer diagram) but on a general (possibly higher-genus) Riemann surface, of the kind introduced in [21]. This resulting BFT is related to the original one by a simple operation, which can be regarded as the direct backreaction of the D-brane instanton on the gauge theory. We review the backreaction of instantons in the mirror of these systems, to lay the ground for their novel discussion in the dimer diagram, and the connection with general BFTs
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