A large N duality via a geometric transition

By F. Cachazo, K. Intriligator, C. Vafa. 2001

434 citations recorded by the source corpus.

Abstract We propose a large N dual of 4d, N =1 supersymmetric, SU ( N ) Yang–Mills with adjoint field Φ and arbitrary superpotential W ( Φ ). The field theory is geometrically engineered via D-branes partially wrapped over certain cycles of a non-trivial Calabi–Yau geometry. The large N , or low-energy, dual arises from a geometric transition of the Calabi–Yau, where the branes have disappeared and have been replaced by suitable fluxes. This duality yields highly non-trivial exact results for the gauge theory. The predictions indeed agree with expected results in cases where it is possible to use standard techniques for analyzing the strongly coupled, supersymmetric gauge theories. Moreover, the proposed large N dual provides a simpler and more unified approach for obtaining exact results for this class of supersymmetric gauge theories.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/daa92e430bd8f52d2c557556dccb9e6915cc5745

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In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. E. Witten
5. Mina Aganagic
6. N. Seiberg
7. R. Dijkgraaf
8. Sergei Gukov

Citations in the corpus

• The C-deformation of gluino and non-planar diagrams (2003, background): “Some of these predictions (coming from genus 0 computations on the closed string side) relate to the superpotential for the glueball fields [7].”
• Geometric Transitions and N=1 Quiver Theories (2001, background): “The story from this point onward is identical to the analysis of [5].”
• Gravitational corrections in supersymmetric gauge theory and matrix models (2002, methodology): “The 3 Note that the sums in the expressions for the periods S1 and Π1 in appendix B of [19] should read ∑ ∞ n=1 cn∆ 2n 21 F (0) (2n−2)! and ∑ ∞ n=1 cn∆ 2n 21 G (0) (2n−2)! , respectively.”
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory (2002, methodology): “For example, we determine the classical relations and quantum deformations of the chiral ring of N = 1 super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.”
• Perturbative analysis of gauged matrix models (2002, positive): “It was shown in [1,2,3], building on previous work [4,5,6,7], that the planar diagrams of the matrix model effectively compute the exact glueball superpotential for the associated supersymmetric gauge theory and thus yield, upon extremization, exact results for the gauge theory.”
• Brane/Flux Annihilation and the String Dual of a Non-Supersymmetric Field Theory (2001, background): “this process via NS 5 brane nucleation may also play an important role in those transitions, which encode the information about D-brane gauge theories in terms of dual geometries with fluxes (see e.g. [4, 20]). In most of this paper, we have restricted our attention to the infrared physics of the mod”
• A Geometric unification of dualities (2001, methodology): “Dynamics of the theory It was shown in [13] for the G = A1 quiver theory case that (6.”
• Les Houches lectures on matrix models and topological strings (2004, methodology): “To do that, we introduce an arbitrary polynomial of degree n + 1 on Φ0, W (Φ0), and we modify the gluing rules above as follows [15]: z′ = 1/z, Φ0 = Φ0, Φ ′ 1 = z (2)Φ1 +W (Φ0)z.”
• A Perturbative Window into Non-Perturbative Physics (2002, methodology): “This unexpected result, that follows straightforwardly from string theory, is completely in accord with field theory arguments, as was shown in [10,17].”
• Holomorphic anomaly in gauge theories and matrix models (2006, methodology): “In section 3 we apply the holomorphic anomaly equations to N = 1 4d gauge theory in a geometry proposed by [4].”
• Matrix models, geometric engineering and elliptic genera (2003, result): “Also consideration of type IIB (and topological B-model) geometries with wrapped and spacetime filling branes leads to exact results for N = 1 supersymmetric gauge theories [3, 4], which is also equivalent to the matrix model realization of a perturbative window into nonperturbative dynamics of thes”
• Chiral Rings and Phases of Supersymmetric Gauge Theories (2003, methodology): “18) This genus n − 1 Riemann surface was introduced in [6].”
• Matrix models, topological strings, and supersymmetric gauge theories (2002, background): “As discussed in [13] in this case the reduction of holomorphic 3-form leads to p− 1 1-forms ηi which naturally get identified with the p− 1 eigenvalue densities in a (p−1) matrix model.”
• Topological Strings and Integrable Hierarchies (2003, background): “Then as conjectured in [22] this undergoes a transition to a geometry with n S(3)’s replacing the n P(1)’s zw − p(2) +W (x)(2) + f(x) = 0, where f(x) is a polynomial of degree n−1 in x, whose coefficients are fixed by the condition that the size of each S(3) is Si = Nigs.”
• All Loop Topological String Amplitudes from Chern-Simons Theory (2002, background): “This was further studied in [14,15], and also in a related context in [16,17,18,19,20,21,22,23].”