Toric duality is Seiberg duality
By C. Beasley, M. R. Plesser. 2001
200 citations recorded by the source corpus.
We study four N = 1 SU(N) 6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP3 which is the blowup of P 2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class | an example of a phenomenon that has been termed \toric duality". However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that the four gauge theories are related by the N = 1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We flnally demonstrate that the other known examples of toric duality are related by N = 1 duality, a fact which we conjecture holds generally.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/00d6d5a19c6b01eebb9d6d02582fc8ea3b0eee56
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Citations in the corpus
- Dimer models and toric diagrams (2005, background): “The non-uniqueness phenomenon is called “Toric duality” [9] and is found to be equivalent to Seiberg duality [10, 11, 12].”
- 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].”
- Seiberg Duality for Quiver Gauge Theories (2002, methodology): “These subtleties indeed appeared for the toric dual theories considered by [6].”
- Counting BPS operators in gauge theories: quivers, syzygies and plethystics (2006, background): “Interesting duality structures of these theories have been expounded in [12, 13, 14, 15].”
- Derived equivalences from mutations of quivers with potential (2009, background): “3 of [6], Section 6 of [15] and Section 3 of [35].”
- Quivers, tilings, branes and rhombi (2005, background): “These “phases” of the theory are believed to be Seiberg–dual to each other [55, 56, 57, 58].”
- Toric duality as Seiberg duality and brane diamonds (2001, unknown): “We begin with an illustrative example that will demonstrate how Seiberg Duality is realised as toric duality.”
- Cluster categories (2010, background): “Then a mutation μi(Q,W ) is defined in [39] (see also [13]), when i does not lie on a 2-cycle.”
- A Geometric unification of dualities (2001, methodology): “related to each other by Seiberg duality were studied there. In the notation of [ 20 ] consider”
- Brane tilings and their applications (2008, background): “This phenomena is dubbed “toric duality”, and it is believed [59] that this is related to the Seiberg duality [60].”
- Brane dimers and quiver gauge theories (2005, background): “It was then realized that partial resolution of these orbifold spaces corresponds to Higgsing the quivers; in this manner, people were able to obtain many different quiver theories and their dual toric geometries [8, 9, 10].”
- Symmetries of Toric Duality (2002, methodology): “This is of course the same as the one given in [9, 8].”