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From matrices to strings and back

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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

  1. R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence, Adv. Theor. Math. Phys. 3 (1999) 1415 [hep-th/9811131] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  2. H. Ooguri and C. Vafa, Worldsheet Derivation of a Large-N Duality, Nucl. Phys. B 641 (2002) 3 [hep-th/0205297] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys Diff. Geom. 1 (1991) 243 [SPIRES].

    MathSciNet  Google Scholar 

  4. M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys. 147 (1992) 1 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. 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].

    Article  MathSciNet  ADS  Google Scholar 

  6. R. Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory, hep-th/9201003 [SPIRES].

  7. P.H. Ginsparg and G.W. Moore, Lectures on 2 − D gravity and 2 − D string theory, hep-th/9304011 [SPIRES].

  8. I.R. Klebanov, String theory in two-dimensions, hep-th/9108019 [SPIRES].

  9. N. Berkovits, A New Limit of the AdS 5 × S 5 σ-model, JHEP 08 (2007) 011 [hep-th/0703282] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. N. Berkovits and C. Vafa, Towards a Worldsheet Derivation of the Maldacena Conjecture, JHEP 03 (2008) 031 [arXiv:0711.1799] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. N. Berkovits, Perturbative super-Yang-Mills from the Topological AdS 5 × S 5 σ-model, JHEP 09 (2008) 088 [arXiv:0806.1960] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. N. Berkovits, Simplifying and Extending the AdS 5 × S 5 Pure Spinor Formalism, JHEP 09 (2009) 051 [arXiv:0812.5074] [SPIRES].

    Article  ADS  Google Scholar 

  13. K. Strebel, Quadratic differentials, Springer-Verlag, New York U.S.A. (1984).

    MATH  Google Scholar 

  14. M. Mulase and M. Penkava, Ribbon graphs, quadratic differentials on riemann surfaces, and algebraic curves defined over \(\bar{q} \), math-ph/9811024.

  15. D. Zvonkine, Strebel differentials on stable curves and kontsevich’s proof of witten’s conjecture, math.AG/0209071.

  16. S.B. Giddings and E.J. Martinec, Conformal Geometry and String Field Theory, Nucl. Phys. B 278 (1986) 91 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. B. Zwiebach, Closed string field theory: Quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. S. Mukhi, Topological matrix models, Liouville matrix model and c = 1 string theory, hep-th/0310287 [SPIRES].

  19. A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers and matrix models. I, math/0101147.

  20. A. Okounkov, Random trees and moduli of curves, math/0309075.

  21. R. Gopakumar, From free fields to AdS. III, Phys. Rev. D 72 (2005) 066008 [hep-th/0504229] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  22. R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  23. R. Gopakumar, From free fields to AdS. II, Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  24. K. Furuuchi, From free fields to AdS: Thermal case, Phys. Rev. D 72 (2005) 066009 [hep-th/0505148] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  25. 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].

    Article  MathSciNet  ADS  Google Scholar 

  26. J.R. David and R. Gopakumar, From spacetime to worldsheet: Four point correlators, JHEP 01 (2007) 063 [hep-th/0606078] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. 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].

    MathSciNet  ADS  Google Scholar 

  28. 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].

    Article  MathSciNet  ADS  Google Scholar 

  29. J.R. David, R. Gopakumar and A. Mukhopadhyay, Worldsheet Properties of Extremal Correlators in AdS/CFT, JHEP 10 (2008) 029 [arXiv:0807.5027] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. S.S. Razamat, On a worldsheet dual of the Gaussian matrix model, JHEP 07 (2008) 026 [arXiv:0803.2681] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [SPIRES].

    Article  ADS  Google Scholar 

  32. R.C. Penner, Perturbative series and the moduli space of Riemann surfaces, J. Diff. Geom. 27 (1988) 35.

    MATH  MathSciNet  Google Scholar 

  33. S.K. Ashok, F. Cachazo and E. Dell’Aquila, Strebel differentials with integral lengths and Argyres- Douglas singularities, hep-th/0610080 [SPIRES].

  34. A.S. Alexandrov, A. Mironov and A. Morozov, Instantons and merons in matrix models, Physica D 235 (2007) 126 [hep-th/0608228] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  35. L. Chekhov, Matrix models: A Way to quantum moduli spaces, hep-th/9305019 [SPIRES].

  36. N. Itzhaki and J. McGreevy, The large-N harmonic oscillator as a string theory, Phys. Rev. D 71 (2005) 025003 [hep-th/0408180] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  37. D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY, 11794-3840, U.S.A.

    Shlomo S. Razamat

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  1. Shlomo S. Razamat
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Correspondence to Shlomo S. Razamat.

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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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