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Higher equations of motion in boundary Liouville field theory

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Abstract

In addition to the ordinary bulk higher equations of motion in the boundary version of the Liouville conformal field theory, an infinite set of relations containing the boundary operators is found. These equations are in one-to-one correspondence with the singular representations of the Virasoro algebra. We comment on the possible applications in the context of minimal boundary Liouville gravity.

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References

  1. A. Zamolodchikov, Higher equations of motion in Liouville field theory, Int. J. Mod. Phys. A 19S2 (2004) 510 [hep-th/0312279] [SPIRES].

    MathSciNet  Google Scholar 

  2. A.B. Zamolodchikov, On the three-point function in minimal Liouville gravity, hep-th/0505063 [SPIRES].

  3. A. Belavin, and A. Zamolodchikov, Polyakov’s string: Twenty five years after, hep-th/0510214 [SPIRES].

  4. A. Belavin and V. Belavin, Four-point function in Super Liouville Gravity, J. Phys. A 42 (2009) 304003 [arXiv:0810.1023] [SPIRES].

    MathSciNet  Google Scholar 

  5. V.A. Belavin, Modular Integrals in Minimal Super Liouville Gravity, Theor. Math. Phys. 161 (2009) 1361 [arXiv:0902.4407] [SPIRES].

    Article  Google Scholar 

  6. V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. I: Boundary state and boundary two-point function, hep-th/0001012 [SPIRES].

  7. J.L. Cardy, Conformal Invariance and Surface Critical Behavior, Nucl. Phys. B 240 (1984) 514 [SPIRES].

    Article  ADS  Google Scholar 

  8. H. Dorn and H.J. Otto, Two and three point functions in Liouville theory, Nucl. Phys. B 429 (1994) 375 [hep-th/9403141] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. A.B. Zamolodchikov and A.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. K. Hosomichi, Bulk-boundary propagator in Liouville theory on a disc, JHEP 11 (2001) 044 [hep-th/0108093] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. B. Ponsot and J. Teschner, Boundary Liouville field theory: Boundary three point function, Nucl. Phys. B 622 (2002) 309 [hep-th/0110244] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. V.G. Kac, Infinite-dimensional Lie algebras, Prog. Math., Vol.44, Birkhäuser, Boston U.S.A. (1983).

    MATH  Google Scholar 

  13. B.L. Feigin, D.B. Fuchs, Representation of the Virasoro algebra, in: A.M. Vershik, D.P. Zhelobenko, editors, Representations of Lie groups and related topics, Adv. Stud. Contemp. Math., Gordon and Breach, New York U.S.A. (1990) 465.

    Google Scholar 

  14. V.S. Dotsenko and V.A. Fateev, Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c < 1, Nucl. Phys. B 251 (1985) 691 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. M. Goulian and M. Li, Correlation functions in Liouville theory, Phys. Rev. Lett. 66 (1991) 2051 [SPIRES].

    Article  ADS  Google Scholar 

  16. A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207 [SPIRES].

    MathSciNet  ADS  Google Scholar 

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

  18. P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2 − D Gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [SPIRES].

    Article  ADS  Google Scholar 

  19. K. Hosomichi, Minimal Open Strings, JHEP 06 (2008) 029 [arXiv:0804.4721] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. J. Polchinski, String Theory, Cambridge University Press, Cambridge U.K. (1998).

    Google Scholar 

  21. E. Witten, Ground ring of two-dimensional string theory, Nucl. Phys. B 373 (1992) 187 [hep-th/9108004] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. D. Kutasov, E.J. Martinec and N. Seiberg, Ground rings and their modules in 2 − D gravity with c <= 1 matter, Phys. Lett. B 276 (1992) 437 [hep-th/9111048] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  23. M.R. Douglas et al., A new hat for the c = 1 matrix model, hep-th/0307195 [SPIRES].

  24. N. Seiberg and D. Shih, Branes, rings and matrix models in minimal (super)string theory, JHEP 02 (2004) 021 [hep-th/0312170] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Belavin and V. Belavin, Four-point function in Super Liouville Gravity, J. Phys. A 42 (2009) 304003 [arXiv:0810.1023] [SPIRES].

    MathSciNet  Google Scholar 

  26. E.W. Barnes, The theory of the dougle gamma function, Phil. Trans. Roy. Soc. A 196 (1901) 265.

    ADS  Google Scholar 

  27. V.S. Dotsenko and V.A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl. Phys. B 240 (1984) 312 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. V.S. Dotsenko and V.A. Fateev, Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c < 1, Nucl. Phys. B 251 (1985) 691 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia

    A. Belavin

  2. Institute of Theoretical and Experimental Physics and Theory Department, Lebedev Physical Institute, RAS, Moscow, Russia

    V. Belavin

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  1. A. Belavin
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  2. V. Belavin
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Correspondence to A. Belavin.

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ArXiv ePrint: 0911.4597

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Belavin, A., Belavin, V. Higher equations of motion in boundary Liouville field theory. J. High Energ. Phys. 2010, 10 (2010). https://doi.org/10.1007/JHEP02(2010)010

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