Geometric Transitions and N=1 Quiver Theories

By F. Cachazo, Sheldon Katz, C. Vafa. 2001

182 citations recorded by the source corpus.

We construct N=1 supersymmetric theories on worldvolumes of D5 branes wrapped around 2-cycles of threefolds which are A-D-E fibrations over a plane. We propose large N duals as geometric transitions involving blowdowns of two cycles and blowups of three-cycles. This yields exact predictions for a large class of N=1 supersymmetric gauge systems including U(N) gauge theories with two adjoint matter fields deformed by superpotential terms, which arise in A-D-E fibered geometries with non-trivial monodromies.

Subfields: Algebra and Number Theory, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3071e8829ffadeda144919a6bf965a3c9ef8f386

How researchers see this paper

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In Algebra and Number Theory

1. C. Vafa
2. R. Dijkgraaf
3. Marcos Mariño
4. F. Cachazo
5. Sheldon Katz
6. A. Klemm
7. N. Orantin
8. B. Eynard

In Mathematical Physics

1. Marcos Mariño
2. C. Vafa
3. Mina Aganagic
4. A. Klemm
5. R. Dijkgraaf
6. B. Eynard
7. E. Witten
8. F. Cachazo

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. R. Dijkgraaf
6. B. Eynard
7. Pavel Putrov
8. N. Seiberg

Citations in the corpus

• On geometry and matrix models (2002, background): “In the case of an Ar quiver there is a more straightforward description of the saddle points [7,8,9].”
• A Geometric unification of dualities (2001, background): “For the case of affine quiver diagrams, the vacua are similarly labeled by the positive affine roots [17].”
• All Loop Topological String Amplitudes from Chern-Simons Theory (2002, background): “In fact a large class of local Calabi-Yau threefolds were constructed in [18] as duals to gauge systems, which were analyzed in [19].”
• N=1 and N=2 Geometry from Fluxes (2002, background): “Let us also introduce a one form h for the reduction of H, h = ∫ S2 H. Note that h is subject to constraints coming from (3.4), namely, ∮ αi h = Ni and ∫ Ci h = τYM → ∮ Ci−Cj h = 0 (3.9) for all i and j in {1, . . . , n}.”
• Topological Strings and Integrable Hierarchies (2003, methodology): “By generalizing to matrix chains, more precisely quiver matrix models of type Ar−1 [28,29,5], one obtains curves that are r-folded covers of the eigenvalue x-plane given by a schematic equation of the form”
• A Perturbative Window into Non-Perturbative Physics (2002, background): “For example, as a first step in this direction, in [13] a quiver gauge theory is described with two adjoints and a tree-level superpotential”
• Les Houches lectures on matrix models and topological strings (2004, background): “branes wrapping two-spheres [16, 14], and the string field theory description reduces to the ADE matrix models considered in [46].”
• Calabi-Yau algebras (2006, unknown): “ t→δ = P x∈Q [x,x ∗], x∗ →∂Φ/∂x, x→0 ∀x∈Q. 4.3. N= 1 super-symmetric quiver gauge theory. An important class of examples is obtained from a ‘nongraded’ analogue of the algebra D(CQ,Φ) as follows, see [CKV]. Fix a quiver Qwith vertex set I. Let F := CQb∼=CQ∗R R[t],cf. (4.2.1). Given an element f∈R[t]”
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems (2009, background): “In the case of An−1 quiver matrix model there are r = n − 1 matrices and the CY geometry takes the form [25]”