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Domain walls for two-dimensional renormalization group flows

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Abstract

Renormalization Group domain walls are natural conformal interfaces between two CFTs related by an RG flow. The RG domain wall gives an exact relation between the operators in the UV and IR CFTs. We propose an explicit algebraic construction of the RG domain wall between consecutive Virasoro minimal models in two dimensions. Our proposal passes a stringent test: it reproduces in detail the leading order mixing of UV operators computed in the conformal perturbation theory literature. The algebraic construction can be applied to a variety of known RG flows in two dimensions.

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References

  1. C. Bachas, J. de Boer, R. Dijkgraaf and H. Ooguri, Permeable conformal walls and holography, JHEP 06 (2002) 027 [hep-th/0111210] [INSPIRE].

    Article  ADS  Google Scholar 

  2. M.R. Douglas, Spaces of quantum field theories, arXiv:1005.2779 [INSPIRE].

  3. E. D’Hoker, J. Estes and M. Gutperle, Interface Yang-Mills, supersymmetry and Janus, Nucl. Phys. B 753 (2006) 16 [hep-th/0603013] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) [arXiv:0807.3720] [INSPIRE].

  5. A. Zamolodchikov, Renormalization group and perturbation theory near fixed points in two-dimensional field theory, Sov. J. Nucl. Phys. 46 (1987) 1090 [INSPIRE].

    MathSciNet  Google Scholar 

  6. S. Fredenhagen and T. Quella, Generalised permutation branes, JHEP 11 (2005) 004 [hep-th/0509153] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. I. Brunner and D. Roggenkamp, Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP 04 (2008) 001 [arXiv:0712.0188] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. I. Brunner, H. Jockers and D. Roggenkamp, Defects and D-brane Monodromies, Adv. Theor. Math. Phys. 13 (2009) 1077 [arXiv:0806.4734] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  9. D. Gaiotto, Surface operators in N = 2 4D gauge theories, JHEP 11 (2012) 090 [arXiv:0911.1316] [INSPIRE].

    Article  ADS  Google Scholar 

  10. T. Quella and V. Schomerus, Symmetry breaking boundary states and defect lines, JHEP 06 (2002) 028 [hep-th/0203161] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. T. Quella, Asymmetrically gauged coset theories and symmetry breaking D-branes: New boundary conditions in conformal field theory, Ph.D. thesis, Humboldt-Universität zu Berlin, Germany (2003).

  12. T. Quella, I. Runkel and G.M. Watts, Reflection and transmission for conformal defects, JHEP 04 (2007) 095 [hep-th/0611296] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. F. Ravanini, Thermodynamic Bethe ansatz for G(k) × G(l)/G(k + l) coset models perturbed by their ϕ (1, 1, Adj) operator, Phys. Lett. B 282 (1992) 73 [hep-th/9202020] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. S. Fredenhagen, M.R. Gaberdiel and C. Schmidt-Colinet, Bulk flows in Virasoro minimal models with boundaries, J. Phys. A 42 (2009) 495403 [arXiv:0907.2560] [INSPIRE].

    MathSciNet  Google Scholar 

  15. A. Zamolodchikov, Higher order integrals of motion in two-dimensional models of the field theory with a broken conformal symmetry, JETP Lett. 46 (1987) 160 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  16. M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011)066007 [arXiv:1011.2986] [INSPIRE].

    ADS  Google Scholar 

  17. J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Duality and defects in rational conformal field theory, Nucl. Phys. B 763 (2007) 354 [hep-th/0607247] [INSPIRE].

    Article  ADS  Google Scholar 

  18. J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Kramers-Wannier duality from conformal defects, Phys. Rev. Lett. 93 (2004) 070601 [cond-mat/0404051] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. C. Crnkovic, R. Paunov, G. Sotkov and M. Stanishkov, Fusions of conformal models, Nucl. Phys. B 336 (1990) 637 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. V. Fateev and A. Zamolodchikov, Integrable perturbations of Z(N ) parafermion models and O(3) σ-model, Phys. Lett. B 271 (1991) 91 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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  1. Institute for Advanced Study, Einstein Dr, Princeton, NJ, 08540, U.S.A

    Davide Gaiotto

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  1. Davide Gaiotto
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Correspondence to Davide Gaiotto.

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ArXiv ePrint: 1201.0767

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Gaiotto, D. Domain walls for two-dimensional renormalization group flows. J. High Energ. Phys. 2012, 103 (2012). https://doi.org/10.1007/JHEP12(2012)103

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  • DOI: https://doi.org/10.1007/JHEP12(2012)103

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