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\(T\overline T \) Deformation and the Light-Cone Gauge

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Abstract

The homogeneous inviscid Burgers equation, which determines the spectrum of a \(T\overline T \) deformed model, has a natural interpretation as the condition of the gauge invariance of the target space-time energy and momentum of a (non-critical) string theory quantised in a generalised uniform light-cone gauge which depends on the deformation parameter. As a simple application of the light-cone gauge interpretation, we derive the \(T\overline T \) deformed Lagrangian for a system of any number of scalars, fermions and chiral bosons with an arbitrary potential. We find that the \(T\overline T \) deformation is driven by the canonical Noether stress-energy tensor but not the covariant one.

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References

  1. L. F. Alday, G. Arutyunov, and S. Frolov, “New integrable system of 2dim fermions from strings on AdS5x S5,” J. High Energy Phys. 2006 (01), 078 (2006); arXiv: hep-th/0508140.

    Google Scholar 

  2. G. Arutyunov and S. Frolov, “Integrable hamiltonian for classical strings on AdS5 × S5,” J. High Energy Phys. 2005 (02), 059 (2005); arXiv: hep-th/0411089.

    Google Scholar 

  3. G. Arutyunov and S. Frolov, “On AdS5 × S5 string S-matrix,” Phys. Lett. B 639 (3-4), 378–382 (2006); arXiv: hep-th/0604043.

    Google Scholar 

  4. G. Arutyunov and S. Frolov, “1) sector,” J. High Energy Phys. 2006 (01), 055 (2006); arXiv: hep-th/0510208.

    Google Scholar 

  5. G. Arutyunov and S. Frolov, “Foundations of the AdS5 × S5 superstring. I,” J. Phys. A: Math. Theor. 42 (25), 254003 (2009); arXiv: 0901.4937 [hep-th].

    MATH  Google Scholar 

  6. G. Arutyunov, S. Frolov, and M. Zamaklar, “Finite-size effects from giant magnons,” Nucl. Phys. B 778 (1–2), 1–35 (2007); arXiv: hep-th/0606126.

    MathSciNet  MATH  Google Scholar 

  7. G. Arutyunov, S. Frolov, and M. Zamaklar, “The Zamolodchikov-Faddeev algebra for AdS5 × S5 superstring,” J. High Energy Phys. 2007 (04), 002 (2007); arXiv: hep-th/0612229.

    Google Scholar 

  8. G. Arutyunov and S. J. van Tongeren, “Double Wick rotating Green-Schwarz strings,” J. High Energy Phys. 2015 (05), 027 (2015); arXiv: 1412.5137 [hep-th].

    MathSciNet  MATH  Google Scholar 

  9. M. Baggio and A. Sfondrini, “Strings on NS-NS backgrounds as integrable deformations,” Phys. Rev. D 98 (2), 021902 (2018); arXiv: 1804.01998 [hep-th].

    Google Scholar 

  10. M. Baggio, A. Sfondrini, G. Tartaglino-Mazzucchelli, and H. Walsh, “On \(T\overline T \) deformations and supersymmetry,” J. High Energy Phys. 2019 (06), 063 (2019); arXiv: 1811.00533 [hep-th].

    Google Scholar 

  11. G. Bonelli, N. Doroud, and M. Zhu, “\(T\overline T \)-deformations in closed form,” J. High Energy Phys. 2018 (06), 149 (2018); arXiv: 1804.10967 [hep-th].

    MATH  Google Scholar 

  12. J. Cardy, “\(T\overline T \) deformations of non-Lorentz invariant field theories,” arXiv: 1809.07849 [hep-th].

  13. M. Caselle, D. Fioravanti, F. Gliozzi, and R. Tateo, “Quantisation of the effective string with TBA,” J. High Energy Phys. 2013 (07), 071 (2013); arXiv: 1305.1278 [hep-th].

    MathSciNet  MATH  Google Scholar 

  14. A. Cavagliä, S. Negro, I. M. Szécsényi, and R. Tateo, “\(T\overline T \)-deformed 2D quantum field theories,” J. High Energy Phys. 2016 (10), 112 (2016); arXiv: 1608.05534 [hep-th].

    MATH  Google Scholar 

  15. C.-K. Chang, C. Ferko, and S. Sethi, “Supersymmetry and \(T\overline T \) deformations,” J. High Energy Phys. 2019 (04), 131 (2019); arXiv: 1811.01895 [hep-th].

    MATH  Google Scholar 

  16. R. Conti, L. lännellä, S. Negro, and R. Tateo, “Generalised Born-Infeld models, Lax operators and the \({\rm{T}}\overline {\rm{T}} \) perturbation,” J. High Energy Phys. 2018 (11), 007 (2018); arXiv: 1806.11515 [hep-th].

    Google Scholar 

  17. R. Conti, S. Negro, and R. Tateo, “The \({\rm{T}}\overline {\rm{T}} \) perturbation and its geometric interpretation,” J. High Energy Phys. 2019 (02), 085 (2019); arXiv: 1809.09593 [hep-th].

    Google Scholar 

  18. R. Conti, S. Negro, and R. Tateo, “Conserved currents and \({\rm{T}}{\overline {\rm{T}} _s}\) irrelevant deformations of 2D integrable field theories,” J. High Energy Phys. 2019 (11), 120 (2019); arXiv: 1904.09141 [hep-th].

    Google Scholar 

  19. A. Dei and A. Sfondrini, “Integrable spin chain for stringy Wess-Zumino-Witten models,” J. High Energy Phys. 2018 (07), 109 (2018); arXiv: 1806.00422 [hep-th].

    MathSciNet  MATH  Google Scholar 

  20. A. Dei and A. Sfondrini, “Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model,” J. High Energy Phys. 2019 (02), 072 (2019); arXiv: 1812.08195 [hep-th].

    Google Scholar 

  21. S. Dubovsky, R. Flauger, and V. Gorbenko, “Solving the simplest theory of quantum gravity,” J. High Energy Phys. 2012 (09), 133 (2012); arXiv: 1205.6805 [hep-th].

    MathSciNet  MATH  Google Scholar 

  22. S. Dubovsky, V. Gorbenko, and G. Hernández-Chifflet, “\(T\overline T \) partition function from topological gravity,” J. High Energy Phys. 2018 (09), 158 (2018); arXiv: 1805.07386 [hep-th].

    MATH  Google Scholar 

  23. S. Dubovsky, V. Gorbenko, and M. Mirbabayi, “Asymptotic fragility, near AdS2 holography and \(T\overline T \),” J. High Energy Phys. 2017 (09), 136 (2017); arXiv: 1706.06604 [hep-th].

    MATH  Google Scholar 

  24. S. Frolov, J. Plefka, and M. Zamaklar, “The AdS5 × S5 superstring in light-cone gauge and its Bethe equations,” J. Phys. A: Math. Gen. 39 (41), 13037–13081 (2006); arXiv: hep-th/0603008.

    MATH  Google Scholar 

  25. M. Guica, “An integrable Lorentz-breaking deformation of two-dimensional CFTs,” SciPost Phys. 5 (5), 048 (2018); arXiv: 1710.08415 [hep-th].

    Google Scholar 

  26. C. M. Hull, “Lectures on W-gravity, W-geometry and W-strings,” in 1992 Summer School in High Energy Physics and Cosmology (World Scientific, Singapore, 1993), ICTP Ser. Theor. Phys. 9, pp. 76–142; Preprint QMW-93-02 (Queen Mary Westfield Coll., London, 1993); arXiv: hep-th/9302110}

    Google Scholar 

  27. H. Jiang, A. Sfondrini, and G. Tartaglino-Mazzucchelli, “\(T\overline T \) deformations with N = (0, 2) supersymmetry,” Phys. Rev. D 100 (4), 046017 (2019); arXiv: 1904.04760 [hep-th].

    MathSciNet  Google Scholar 

  28. Y. Jiang, “Lectures on solvable irrelevant deformations of 2d quantum field theory,” arXiv: 1904.13376 [hep-th].

  29. T. Klose, T. McLoughlin, R. Roiban, and K. Zarembo, “Worldsheet scattering in AdS5 × S5,” J. High Energy Phys. 2007 (03), 094 (2007); arXiv: hep-th/0611169.

    Google Scholar 

  30. T. Klose and K. Zarembo, “Bethe ansatz in stringy sigma models,” J. Stat. Mech. 2006 (05), P05006 (2006); arXiv: hep-th/0603039.

    MathSciNet  MATH  Google Scholar 

  31. M. Kruczenski and A. A. Tseytlin, “Semiclassical relativistic strings in S5 and long coherent operators in N = 4 SYM theory,” J. High Energy Phys. 2004 (09), 038 (2004); arXiv: hep-th/0406189.

    Google Scholar 

  32. J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2 (2), 231–252 (1998); Int. J. Theor. Phys. 38, 1113–1133 (1999); arXiv: hep-th/9711200.

    MathSciNet  MATH  Google Scholar 

  33. A. Melikyan, E. Pereira, and V. O. Rivelles, “On the equivalence theorem for integrable systems,” J. Phys. A: Math. Theor. 48 (12), 125204 (2015); arXiv: 1412.1288 [hep-th].

    MathSciNet  MATH  Google Scholar 

  34. A. Melikyan, A. Pinzul, V. O. Rivelles, and G. Weber, “Quantum integrability of the Alday-Arutyunov-Frolov model,” J. High Energy Phys. 2011 (09), 092 (2011); arXiv: 1106.0512 [hep-th].

    MathSciNet  MATH  Google Scholar 

  35. A. Melikyan and G. Weber, “The r-matrix of the Alday-Arutyunov-Frolov model,” J. High Energy Phys. 2012 (11), 165 (2012); arXiv: 1209.6042 [hep-th].

    Google Scholar 

  36. A. Melikyan and G. Weber, “Integrable theories and generalized graded Maillet algebras,” J. Phys. A: Math. Theor. 47 (6), 065401 (2014); arXiv: 1307.2831 [hep-th].

    MathSciNet  MATH  Google Scholar 

  37. A. Melikyan and G. Weber, “On the quantization of continuous non-ultralocal integrable systems,” Nucl. Phys. B 913, 716–746 (2016); arXiv: 1611.02622 [hep-th].

    MATH  Google Scholar 

  38. S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet,” Phys. Rev. Lett. 70 (21), 3339–3342 (1993); arXiv: cond-mat/9212030.

    Google Scholar 

  39. F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories,” Nucl. Phys. B 915, 363–383 (2017); arXiv: 1608.05499 [hep-th].

    MathSciNet  MATH  Google Scholar 

  40. A. B. Zamolodchikov, “Expectation value of composite field \(T\overline T \) in two-dimensional quantum field theory,” arXiv: hep-th/0401146.

  41. K. Zarembo, “Worldsheet spectrum in AdS4/CFT3 correspondence,” J. High Energy Phys. 2009 (04), 135 (2009); arXiv: 0903.1747 [hep-th].

    Google Scholar 

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Acknowledgments

I would like to thank Tristan McLoughlin and Alessandro Sfondrini for fruitful discussions, and Alessandro Sfondrini for useful comments on the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Hamilton Mathematics Institute, Trinity College, 17 Westland Row, Dublin 2, Ireland

    Sergey A. Frolov

  2. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Sergey A. Frolov

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  1. Sergey A. Frolov
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Correspondence to Sergey A. Frolov.

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To Andrei Alekseevich Slavnov, the best supervisor one can hope for, on the occasion of his 80th birthday

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 309, pp. 120–140.

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Frolov, S.A. \(T\overline T \) Deformation and the Light-Cone Gauge. Proc. Steklov Inst. Math. 309, 107–126 (2020). https://doi.org/10.1134/S0081543820030098

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