Bipartite field theories and D-brane instantons

A bstract 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 g...

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Bibliographic Details
Published in:The journal of high energy physics 2018-11, Vol.2018 (11), p.1-43, Article 98
Main Authors: Franco, Sebastián, García-Valdecasas, Eduardo, Uranga, Angel M.
Format: Article
Language:English
Subjects:
Brane Dynamics in Gauge Theories
Branes
Classical and Quantum Gravitation
Combinatorial analysis
D-branes
Deformation effects
Deformation mechanisms
Dimers
Elementary Particles
Field theory
High energy physics
Instantons
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Riemann surfaces
Singularities
String Theory
Supersymmetric Gauge Theory
Tiling
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2018)098