Abstract
We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differentials techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.
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References
R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence, Adv. Theor. Math. Phys. 3 (1999) 1415 [hep-th/9811131] [SPIRES].
H. Ooguri and C. Vafa, Worldsheet Derivation of a Large-N Duality, Nucl. Phys. B 641 (2002) 3 [hep-th/0205297] [SPIRES].
E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys Diff. Geom. 1 (1991) 243 [SPIRES].
M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys. 147 (1992) 1 [SPIRES].
D. Gaiotto and L. Rastelli, A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model, JHEP 07 (2005) 053 [hep-th/0312196] [SPIRES].
R. Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory, hep-th/9201003 [SPIRES].
P.H. Ginsparg and G.W. Moore, Lectures on 2 − D gravity and 2 − D string theory, hep-th/9304011 [SPIRES].
I.R. Klebanov, String theory in two-dimensions, hep-th/9108019 [SPIRES].
N. Berkovits, A New Limit of the AdS 5 × S 5 σ-model, JHEP 08 (2007) 011 [hep-th/0703282] [SPIRES].
N. Berkovits and C. Vafa, Towards a Worldsheet Derivation of the Maldacena Conjecture, JHEP 03 (2008) 031 [arXiv:0711.1799] [SPIRES].
N. Berkovits, Perturbative super-Yang-Mills from the Topological AdS 5 × S 5 σ-model, JHEP 09 (2008) 088 [arXiv:0806.1960] [SPIRES].
N. Berkovits, Simplifying and Extending the AdS 5 × S 5 Pure Spinor Formalism, JHEP 09 (2009) 051 [arXiv:0812.5074] [SPIRES].
K. Strebel, Quadratic differentials, Springer-Verlag, New York U.S.A. (1984).
M. Mulase and M. Penkava, Ribbon graphs, quadratic differentials on riemann surfaces, and algebraic curves defined over \(\bar{q} \), math-ph/9811024.
D. Zvonkine, Strebel differentials on stable curves and kontsevich’s proof of witten’s conjecture, math.AG/0209071.
S.B. Giddings and E.J. Martinec, Conformal Geometry and String Field Theory, Nucl. Phys. B 278 (1986) 91 [SPIRES].
B. Zwiebach, Closed string field theory: Quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [SPIRES].
S. Mukhi, Topological matrix models, Liouville matrix model and c = 1 string theory, hep-th/0310287 [SPIRES].
A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers and matrix models. I, math/0101147.
A. Okounkov, Random trees and moduli of curves, math/0309075.
R. Gopakumar, From free fields to AdS. III, Phys. Rev. D 72 (2005) 066008 [hep-th/0504229] [SPIRES].
R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [SPIRES].
R. Gopakumar, From free fields to AdS. II, Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [SPIRES].
K. Furuuchi, From free fields to AdS: Thermal case, Phys. Rev. D 72 (2005) 066009 [hep-th/0505148] [SPIRES].
O. Aharony, Z. Komargodski and S.S. Razamat, On the worldsheet theories of strings dual to free large-N gauge theories, JHEP 05 (2006) 016 [hep-th/0602226] [SPIRES].
J.R. David and R. Gopakumar, From spacetime to worldsheet: Four point correlators, JHEP 01 (2007) 063 [hep-th/0606078] [SPIRES].
O. Aharony, J.R. David, R. Gopakumar, Z. Komargodski and S.S. Razamat, Comments on worldsheet theories dual to free large-N gauge theories, Phys. Rev. D 75 (2007) 106006 [hep-th/0703141] [SPIRES].
I. Yaakov, Open and closed string worldsheets from free large-N gauge theories with adjoint and fundamental matter, JHEP 11 (2006) 065 [hep-th/0607244] [SPIRES].
J.R. David, R. Gopakumar and A. Mukhopadhyay, Worldsheet Properties of Extremal Correlators in AdS/CFT, JHEP 10 (2008) 029 [arXiv:0807.5027] [SPIRES].
S.S. Razamat, On a worldsheet dual of the Gaussian matrix model, JHEP 07 (2008) 026 [arXiv:0803.2681] [SPIRES].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [SPIRES].
R.C. Penner, Perturbative series and the moduli space of Riemann surfaces, J. Diff. Geom. 27 (1988) 35.
S.K. Ashok, F. Cachazo and E. Dell’Aquila, Strebel differentials with integral lengths and Argyres- Douglas singularities, hep-th/0610080 [SPIRES].
A.S. Alexandrov, A. Mironov and A. Morozov, Instantons and merons in matrix models, Physica D 235 (2007) 126 [hep-th/0608228] [SPIRES].
L. Chekhov, Matrix models: A Way to quantum moduli spaces, hep-th/9305019 [SPIRES].
N. Itzhaki and J. McGreevy, The large-N harmonic oscillator as a string theory, Phys. Rev. D 71 (2005) 025003 [hep-th/0408180] [SPIRES].
D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [SPIRES].
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ArXiv ePrint: 0911.0658
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Razamat, S.S. From matrices to strings and back. J. High Energ. Phys. 2010, 49 (2010). https://doi.org/10.1007/JHEP03(2010)049
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DOI: https://doi.org/10.1007/JHEP03(2010)049