D-brane gauge theories from toric singularities and toric duality

By Bo Feng, A. Hanany, Yang-Hui He. 2000

321 citations recorded by the source corpus.

Via partial resolution of Abelian orbifolds we present an algorithm for extracting a consistent set of gauge theory data for an arbitrary toric variety whose singularity a D-brane probes. As illustrative examples, we tabulate the matter content and superpotential for a D-brane living on the toric del Pezzo surfaces as well as the zeroth Hirzebruch surface. Moreover, we discuss the non-uniqueness of the general problem and present examples of vastly different theories whose moduli spaces are described by the same toric data. Our methods provide new tools for calculating gauge theories which flow to the same universality class in the IR. We shall call it “Toric Duality”.

Subfields: Astronomy and Astrophysics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/48bf829b1d3cbdf30e95ef68c324a3f49bb3d44d

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Citations in the corpus

Toric duality as Seiberg duality and brane diamonds (2001, unknown): “This also solves the old question [7, 9] that the Inverse Algorithm does not in principle tell us how”
Tilings, Chern-Simons Theories and M2 Branes (2008, background): “A natural question is if all toric CalabiYau singularities arise in this way and how to find the inverse algorithm, that in 3+1 dimensions is developed in [48, 49, 50].”
Representations of Algebras and Related Topics (2011, background): “is a special case of a family of ‘period 2 solutions’ of [FM09, Section 7.4] with m 1= m 3 = −m 2 = 1 and m ¯ = 0 therein. It is also the quiver for the quiver gauge theory on the del Pezzo 3 surface [FHH01]. See [FM09] for more detail. 3.2. Examples of periodic cluster algebras. Example 3.4. Cluste”
An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals (2004, methodology): “The gauge theory for this geometry was computed in [20] and is also presented in [27].”
$\mathcal{N} = 2$ quantum field theories and their BPS quivers (2011, methodology): “• The toric methods of [46, 47] and the relation to dimer models [48] were used in [49] to construct a large class of quivers, their construction using mirror symmetry was studied in [50].”
Toric duality is Seiberg duality (2001, background): “In this paper, we study some examples of toric dualities, including the examples of [10].”
The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds (2005, methodology): “ a variety of physical and mathematical arguments. In particular, if Y is toric in principle1 there is an algorithm which constructs the gauge theory from the toric data of the Calabi–Yau singularity [18, 19]. Thus in this case both the geometry and the gauge theory are speciﬁed by a set of combinat”
Gauge theories from toric geometry and brane tilings (2005, background): “Although it has been known in principle how to compute toric data dual to a given SCFT and vice versa [36, 37], these computations are often very computationally expensive, even for fairly small quivers.”
Phase structure of D-brane gauge theories and toric duality (2001, methodology): “Y.-H. H. is also supported by the Presidential Fellowship of MIT.”
Fractional branes and dynamical supersymmetry breaking (2005, background): “7.1 Brane tiling perspective of fractional branes 30 7.2 Beta function relations and baryonic U(1) symmetries from brane tilings 35”
Symmetries of Toric Duality (2002, methodology): “The Inverse Algorithm of [6] remains an effective - in the sense of reducing the computations to nothing but linear algebra and integer programming - method of deriving toric (and hence Seiberg) dual theories.”
Brane tilings and their applications (2008, background): “Although general algorithm already existed [61] using partial resolutions, computation often becomes unpractical as the toric diagram becomes more and more complicated.”
Dimer models and toric diagrams (2005, methodology): “They agree with examples calculated in [9, 18, 16], who also observed the pattern of binomial coefficients along the edges of the polygon.”
Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals (2004, methodology): “Given the toric diagram forC(Y) there are methods to construct a superconformal field theory, whose Higgs branch is the toric varietyX ∼= C(Y), purely from the combinatorial data that definesX [11].”