Worldsheet derivation of a large N duality

By Hirosi Ooguri, C. Vafa. 2002

251 citations recorded by the source corpus.

We give a worldsheet proof of the equivalence between the U(N) Chern-Simons gauge theory on S-3 and the topological closed string theory on the resolved conifold geometry. When the 't Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to "holes" on the worldsheet, generating an open string sector. This leads to a microscopic description of how the 't Hooft expansion of gauge theory amplitudes is reproduced in the closed string computation. We find that the closed string amplitudes also contain terms which are not captured in the 't Hooft expansion but are present in the exact computation in the gauge theory amplitudes. These arise when the whole Riemann surface is in the new branch. We also discuss the cases with SO and Sp gauge groups.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e73ec56067cbd646ef211e26f0a01323e2e83270

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Citations in the corpus

Les Houches lectures on matrix models and topological strings (2004, unknown): “G 2(N+2) (2.32) where G2(z) is the Barnes function, deﬁned by G2(z+1) = Γ(z)G2(z), G2(1) = 1. (2.33) Comparing these results, we ﬁnd that ΩN = (2π)N(N−1) 2 G2(N+2) . (2.34) Using now (see for example [59]): vol(U(N)) = (2π)12N(N+1) G2(N+1) . (2.35) we see that 1 vol(U(N)) Z dMf(M) = 1 N! 1 (2π)N Z Y”
Perturbative computation of glueball superpotentials (2002, background): “Note that the full answer for the effective superpotential also includes the Veneziano-Yankielowicz term NS log(S/Λ(3)) [9], which in the matrix model comes from the volume of the gauge group [10].”
The Topological Vertex (2003, background): “As was conjectured in [2] and proven in [31], the topological open string A-model of N D-branes on S in Y = T S is the same as the topological A-model closed string theory on X = O(−1)⊕O(−1) → P.”
The C-deformation of gluino and non-planar diagrams (2003, background): “In particular, the open/closed topological string duality conjectured in [4] and proven in [5] leads to some non-perturbative predictions for N = 1 gauge theories in 4 dimensions constructed as low energy limits of superstring theory [6].”
Liouville Field Theory — A decade after the revolution (2004, background): “The first setup [77], [78] is the duality between a topological open string theory and a closed string theory (and its embedding in the physical superstring theory [79]).”
The Hagedorn - deconfinement phase transition in weakly coupled large N gauge theories (2004, background): “gauge coupling(65), and by the consequent derivation of dualities between (topological) open and closed string theories [70,71].”
Perturbative analysis of gauged matrix models (2002, unknown): “Here the first term receives a contribution from the measure of the unbroken gauge group U(M1) × U(M2) [17], where each factor gives a standard term S(2) i log Si that reproduces 15”
D-Branes on Calabi-Yau Manifolds (2004, unknown): “This “topological gravity” is also important in the “large N” duality of [24, 25].”
Matrix model as a mirror of Chern-Simons theory (2002, background): “…the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N = 1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators.”
SU(N) Geometries and Topological String Amplitudes (2003, background): “(39) This form for the coefficients of the multicovering is not that surprising since the term in the exponential in this case is a refinement of the open string amplitude which is conjectured [23] to have multicovering contribution with coefficients satisfying the above equation.”
Chern-Simons theory and topological strings (2004, unknown): “The nonperturbative piece also admits an asymptotic expansion that can be easily worked out by expanding the Barnes function (Periwal, 1993; Ooguri and Vafa 2002).”
Chiral Rings and Phases of Supersymmetric Gauge Theories (2003, unknown): “For large N̂ the volume of U(N̂) is [40,41],”
Gravity Induced C-Deformation (2003, background): “This conjecture was motivated by the meaning of topological string amplitudes in the context of low energy effective theories of superstring compactifications [4,5,6,7] together with the large N duality conjectures [8], proven in [9] and embedded in superstrings in [7].”
Holomorphic anomaly in gauge theories and matrix models (2006, methodology): “This model also contains a non-perturbative part of free energy defined as the volume factor of the U(N) gauge group as in [47], where it was computed with the following result”
Gravitational corrections in supersymmetric gauge theory and matrix models (2002, unknown): “…lnN − 1 12 lnN − 3 4 N2 + 1 2 N ln 2π + ζ ′(−1) + ∞∑ g=2 B2g 4g(g − 1) 1 N2g−2 (4.11) this becomes Fn.p. = 1 2 N21 ln (N1 m ) + 1 2 N22 ln (N2 m ) − 3 4 (N21 +N 2 2 )− 1 12 ln(N1N2) + 2ζ ′(−1) + ∞∑ g=2 B2g 4g(g − 1) ( 1 N2g−21 + 1 N2g−22 ) (4.12) Comparing with the prepotential of the gauge…”