Symmetries of Toric Duality

By Bo Feng, S. Franco, A. Hanany, Yang-Hui He. 2002

153 citations recorded by the source corpus.

This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7f2aa5de36eb1e53bc120beb3ed2b625ff860e82

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Citations in the corpus

Gauge theories from toric geometry and brane tilings (2005, background): “Roughly, this is because there are necessarily a+3b−(a+b) = 2b terms in the superpotential, and every field must appear precisely twice by the quiver toric condition [62].”
The exact superconformal R-symmetry maximizes a (2003, methodology): “singularity of a local CY which is a complex cone over dP1: W= X21X14X42+ X21X13X32+X21X14X43X32. (4.9) Since we only care about the symmetries, we’ve suppressed the coeﬃcients and ﬂavor indices; see [14] for the precise superpotential. We can think of the resulting SCFT as the IR limit of a RG ﬂow,”
New checks and subtleties for AdS/CFT and a-maximization (2004, background): “2 The quiver gauge theory for the first del Pezzo The quiver gauge theory for dP1 was constructed in [7, 23] and is a four dimensional N = 1 SCFT with gauge group SU(N)(4) and bi-fundamental matter.”
Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals (2004, background): “Let us first remark that, given a toric Gorenstein canonical singularity, an algorithm for constructing21 a quiver gauge theory that has the singularity as its Higgs branch has been developed in [11, 42] and subsequent works by these authors.”
The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds (2005, background): “In particular, if Y is toric in principle(1) there is an algorithm which constructs the gauge theory from the toric data of the Calabi–Yau singularity [18, 19].”
THE MASTER SPACE OF N=1 GAUGE THEORIES (2008, background): “We point out that this model is one of the toric phases (phase II in the notation of [35]), and we shall only consider this one for now.”
Dimer models and toric diagrams (2005, methodology): “The collection of multiplicities which were known so far were summarized in [16].”
An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals (2004, methodology): “We notice that a generic quiver in the Duality Tree will not satisfy the quiver toric condition, i.e. the equality for all the ranks of the gauge groups.”
Seiberg Duality for Quiver Gauge Theories (2002, methodology): “These techniques have been used to geometrically engineer other singularities and make them tractable from a D-brane analysis; and have led to the notion of toric duality [27, 28, 29, 30, 6] by arriving to different field theories associated to the same singularity by taking different paths to get t”
Brane dimers and quiver gauge theories (2005, methodology): “There corresponding quivers and superpotentianls can be found in [13].”
Dimer models from mirror symmetry and quivering amoebae (2005, background): “We see that the coefficients n! k!(n−k)! are nothing but the linear sigma model field multiplicities conjectured in [37], for the case of colinear points on the boundary of the toric diagram.”
Quivers, tilings, branes and rhombi (2005, background): “2) In general, the number of gauge groups in the quiver, or equivalently, the number of faces in the brane tiling is equal to twice the area of the toric diagram [30].”
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lp,q|r (2005, background): “On the gauge side, the quiver can be thought of as a more explicit description of the algebro-geometric structure of the singularity M3, and an algorithm exists [3], even though it can efficiently handle only small toric polygons; see [4, 5, 6, 7, 8, 10, 9].”
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”
Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “The next simplest class is the toric singularities, the investigation of which was initiated by [8, 9, 10, 11].”