Phase structure of D-brane gauge theories and toric duality

By Bo Feng, A. Hanany, Yang-Hui He. 2001

168 citations recorded by the source corpus.

Harnessing the unimodular degree of freedom in the definition of any toric diagram, we present a method of constructing inequivalent gauge theories which are world-volume theories of D-branes probing the same toric singularity. These theories are various phases in partial resolution of abelian orbifolds. As examples, two phases are constructed for both the zeroth Hirzebruch and the second del Pezzo surfaces. We show that such a phenomenon is a special case of ``Toric Duality'' proposed in hepth0003085. Furthermore, we investigate the general conditions that distinguish these different gauge theories with the same (toric) moduli space.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5f93887e9e0f5f3238c67a2306b3a540aa324be9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. A. Hanany
2. Alberto Zaffaroni
3. M. Yamazaki
4. C. Vafa
5. J. Sparks
6. D. Martelli
7. Yang-Hui He
8. S. Franco

In Nuclear and High Energy Physics

1. A. Hanany
2. Alberto Zaffaroni
3. M. Yamazaki
4. C. Vafa
5. D. Martelli
6. J. Sparks
7. S. Franco
8. Yang-Hui He

In Statistical and Nonlinear Physics

1. M. Yamazaki
2. A. Hanany
3. Alberto Zaffaroni
4. Clay Córdova
5. Yang-Hui He
6. F. Cachazo
7. C. Vafa
8. J. Sparks

Citations in the corpus

• 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”
• Quivers, tilings, branes and rhombi (2005, methodology): “For a complete introduction to brane tilings and to the Fast Forward Algorithm and for more examples the reader should refer to [1, 16].”
• Toric duality as Seiberg duality and brane diamonds (2001, unknown): “the appendix of [8]); also any toric diagram can be embedded into that of such an orbifold (in particular any toric local Calabi-Yau threefold D can be embedded into C/(Zn × Zn) for sufficiently large n.”
• A Geometric unification of dualities (2001, methodology): “The quiver theory for this case is given in [77] and shown in Fig.”
• 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.”
• Dimer models and toric diagrams (2005, background): “They agree with examples calculated in [9, 18, 16], who also observed the pattern of binomial coefficients along the edges of the polygon.”
• Dimer models from mirror symmetry and quivering amoebae (2005, background): “[10, 7]) with the toric diagram and the Newton polynomial given in (2.”
• Toric duality is Seiberg duality (2001, methodology): “the F0 models (the first of which appears in [5], both of which appear in [15]):”
• 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”
• $\mathcal{N} = 2$ 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].”
• 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].”
• Brane tilings and their applications (2008, background): “106) is first studied in such a context in [112], and ρD are interpreted as fields in GLSM(37).”
• Symmetries of Toric Duality (2002, methodology): “In due course we shall see the true nature of toric duality: that the unimodular degree of freedom whence it arises as claimed in [7] - though such unimodularity persists as a symmetry of the theory - is but a special case.”
• THE MASTER SPACE OF N=1 GAUGE THEORIES (2008, methodology): “Looking at the toric diagram one can easily understand that the gauge theory can flow to the one associated to the C/Z2 × C singularity in four different ways by giving We remind the reader that the prescription is as follows [4, 5, 34].”