Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

\( T\overline{T},J\overline{T},T\overline{J} \) partition sums from string theory

  • 15 Accesses

Abstract

We calculate the torus partition sum of a general CFT2 with left and right moving conserved currents J and \( \overline{J} \), perturbed by a combination of the irrelevant operators \( T\overline{T},J\overline{T} \) and \( T\overline{J} \). We use string theory techniques to write it as an integral transform of the partition sum of the unperturbed CFT with chemical potentials for the left and right moving conserved charges. The resulting expression transforms in the right way under the modular group, and reproduces the known spectrum of these models. We also derive a formula for the partition function of deformed CFT2 with non-vanishing chemical potentials.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys.B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].

  2. [2]

    A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \)-deformed 2D Quantum Field Theories, JHEP10 (2016) 112 [arXiv:1608.05534] [INSPIRE].

  3. [3]

    M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys.5 (2018) 048 [arXiv:1710.08415] [INSPIRE].

  4. [4]

    S. Chakraborty, A. Giveon and D. Kutasov, \( J\overline{T} \)deformed CFT2and string theory, JHEP10 (2018) 057 [arXiv:1806.09667] [INSPIRE].

  5. [5]

    L. Apolo and W. Song, Strings on warped AdS3via \( T\overline{J} \)deformations, JHEP10 (2018) 165 [arXiv:1806.10127] [INSPIRE].

  6. [6]

    B. Le Floch and M. Mezei, Solving a family of \( T\overline{T} \)-like theories, arXiv:1903.07606 [INSPIRE].

  7. [7]

    S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{T},J\overline{T},T\overline{J} \)and String Theory, J. Phys.A 52 (2019) 384003 [arXiv:1905.00051] [INSPIRE].

  8. [8]

    O. Aharony, S. Datta, A. Giveon, Y. Jiang and D. Kutasov, Modular invariance and uniqueness of \( T\overline{T} \)deformed CFT, JHEP01 (2019) 086 [arXiv:1808.02492] [INSPIRE].

  9. [9]

    J. Cardy, The \( T\overline{T} \)deformation of quantum field theory as random geometry, JHEP10 (2018) 186 [arXiv:1801.06895] [INSPIRE].

  10. [10]

    S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \)partition function from topological gravity, JHEP09 (2018) 158 [arXiv:1805.07386] [INSPIRE].

  11. [11]

    S. Datta and Y. Jiang, \( T\overline{T} \)deformed partition functions, JHEP08 (2018) 106 [arXiv:1806.07426] [INSPIRE].

  12. [12]

    O. Aharony, S. Datta, A. Giveon, Y. Jiang and D. Kutasov, Modular covariance and uniqueness of \( J\overline{T} \)deformed CFTs, JHEP01 (2019) 085 [arXiv:1808.08978] [INSPIRE].

  13. [13]

    A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \)and LST, JHEP07 (2017) 122 [arXiv:1701.05576] [INSPIRE].

  14. [14]

    A. Giveon, N. Itzhaki and D. Kutasov, A solvable irrelevant deformation of AdS3/CFT2, JHEP12 (2017) 155 [arXiv:1707.05800] [INSPIRE].

  15. [15]

    A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS3 , Adv. Theor. Math. Phys.2 (1998) 733 [hep-th/9806194] [INSPIRE].

  16. [16]

    D. Kutasov and N. Seiberg, More comments on string theory on AdS3 , JHEP04 (1999) 008 [hep-th/9903219] [INSPIRE].

  17. [17]

    D. Kutasov, Geometry on the Space of Conformal Field Theories and Contact Terms, Phys. Lett.B 220 (1989) 153 [INSPIRE].

  18. [18]

    A. Giveon, D. Kutasov and O. Pelc, Holography for noncritical superstrings, JHEP10 (1999) 035 [hep-th/9907178] [INSPIRE].

  19. [19]

    J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string. Cambridge University Press (1998) [INSPIRE].

  20. [20]

    A. Hashimoto and D. Kutasov, Strings, Symmetric Products, \( T\overline{T} \)deformations and Hecke Operators, arXiv:1909.11118 [INSPIRE].

  21. [21]

    A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept.244 (1994) 77 [hep-th/9401139] [INSPIRE].

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Author information

Correspondence to Akikazu Hashimoto.

Additional information

ArXiv ePrint: 1907.07221

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hashimoto, A., Kutasov, D. \( T\overline{T},J\overline{T},T\overline{J} \) partition sums from string theory. J. High Energ. Phys. 2020, 80 (2020). https://doi.org/10.1007/JHEP02(2020)080

Download citation

Keywords

  • Conformal Field Theory
  • Renormalization Group