Advertisement

Journal of High Energy Physics

, 2019:108 | Cite as

λ-deformation of the AdS5 × S5 pure spinor superstring

  • Héctor A. Benítez
  • David M. SchmidttEmail author
Open Access
Regular Article - Theoretical Physics
  • 44 Downloads

Abstract

The lambda deformation of the pure spinor formalism of the superstring in the AdS5 × S5 background is introduced. It is shown that the deformation preserves the integrability as well as the one-loop conformal invariance of its parent theory. It is also shown that the effective action takes the standard form of the Berkovits-Howe action functional, allowing to calculate the deformed background supergeometry in a straightforward way. The background fields coincide with those of the lambda model of the Green-Schwarz formalism, hence satisfying the same set of supergravity equations of motion.

Keywords

Integrable Field Theories Sigma Models Superstrings and Heterotic Strings 

Notes

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

References

  1. [1]
    I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5superstring, Phys. Rev.D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].ADSGoogle Scholar
  2. [2]
    R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5background, Nucl. Phys.B 533 (1998) 109 [hep-th/9805028] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    N. Berkovits and O. Chandía, Superstring vertex operators in an AdS 5 × S 5background, Nucl. Phys.B 596 (2001) 185 [hep-th/0009168] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    B.C. Vallilo, Flat currents in the classical AdS 5 × S 5pure spinor superstring, JHEP03 (2004) 037 [hep-th/0307018] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  5. [5]
    G. Arutyunov and S. Frolov, Foundations of the AdS 5 × S 5superstring. Part I, J. Phys.A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].ADSzbMATHGoogle Scholar
  6. [6]
    C. Klimčík, Yang-Baxter σ-models and dS/AdS T duality, JHEP12 (2002) 051 [hep-th/0210095] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable σ-models, JHEP11 (2013) 192 [arXiv: 1308.3581] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS 5 × S 5superstring action, Phys. Rev. Lett.112 (2014) 051601 [arXiv:1309 .5850] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    F. Delduc, M. Magro and B. Vicedo, Derivation of the action and symmetries of the q-deformed AdS 5 × S 5superstring, JHEP10 (2014) 132 [arXiv: 1406.6286] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5 × S 5superstri ng, JHEP04 (2014) 153 [arXiv:1401.4855] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Matsumoto and K. Yoshida, Integrable deformations of the AdS 5 × S 5superstring and the classical Yang-Baxter equationtowards the gravity/CYBE correspondence, J. Phys. Conf. Ser.563 (2014) 012020 [arXiv:1410. 0575] [INSPIRE].CrossRefGoogle Scholar
  12. [12]
    R. Borsato and L. Wulff, Target space supergeometry of η and λ-deformed strings, JHEP10 (2016) 045 [arXiv:1608. 03570] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    K. Sfetsos, Integrable interpolations: from exact CFTs to non-Abelian T-duals, Nucl. Phys.B 880 (2014) 225 [arXiv:1312 .4560] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, Integrable deformations of strings on symmetric spaces, JHEP11 (2014) 009 [arXiv:1407. 2840] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, S-matrices and quantum group symmetry of k-deformed σ-models, J. Phys.A 49 (2016) 465201 [arXiv:1506. 06601] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  16. [16]
    T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, An integrable deformation of the AdS 5 × S 5superstring, J. Phys.A 47 (2014) 495402 [arXiv:1409 .1538] [INSPIRE].zbMATHGoogle Scholar
  17. [17]
    C. Appadu, T.J. Hollowood, J.L. Miramontes, D. Price and D.M. Schmidtt, Giant magnons of string theory in the lambda background, JHEP07 (2017) 098 [arXiv:1704. 05437] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    R. Borsato, A.A. Tseytlin and L. Wulff, Supergravity background of λ-deformed mod el for AdS 2 × S 2supercoset, Nucl. Phys.B 905 (2016) 264 [arXiv:1601. 08192] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    Y. Chervonyi and O. Lunin, Supergravity background of the λ-deformed AdS 3 × S 3supercoset, Nucl. Phys.B 910 (2016) 685 [arXiv:1606.00394] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S. Demulder, K. Sfetsos and D.C. Thompson, Integrable λ-deformations: squashing coset CFTs and AdS 5 × S 5, JHEP07 (2015) 019 [arXiv:1504.02781] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    C. Klimčík, η and λ deformations as E-models, Nucl. Phys.B 900 (2015) 259 [arXiv:1508.05832] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    B. Vicedo, Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles, J. Phys.A 48 (2015) 355203 [arXiv: 1504.06303] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  23. [23]
    D. Roychowdhury, Analytic integrability for strings on η and λ deformed backgrounds, JHEP10 (2017) 056 [arXiv:1707.07172] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    H.A. Benitez and V.O. Rivelles, Yang-Baxter deformations of the AdS 5 × S 5pure spinor superstring, JHEP02 (2019) 056 [arXiv:1807.10432] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    O.A. Bedoya, L.I. Bevilaqua, A. Mikhailov and V.O. Rivelles, Notes on β-deformations of the pure spinor superstring in AdS 5 × S 5, Nucl. Phys.B 848 (2011) 155 [arXiv:1005.0049] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    D.M. Schmidtt, Exploring the lambda model of the hybrid superstring, JHEP10 (2016) 151 [arXiv:1609.05330] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    M. Magro, The classical exchange algebra of AdS 5 × S 5, JHEP01 (2009) 021 [arXiv:0810. 4136] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    B. Vicedo, Hamiltonian dynamics and the hidden symmetries of the AdS 5 × S 5superstring, JHEP01 (2010) 102 [arXiv :0910. 0221] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    D.M. Schmidtt, Integrable lambda models and Chern-Simons theories, JHEP 05 (2017) 012 [arXiv:1701.04138] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    D.M. Schmidtt, Lambda models from Chern-Simons theories, JHEP11 (2018) 111 [arXiv:1808. 05994] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    J.M. Maillet, New integrable canonical structures in two-dimensional models, Nucl. Phys.B 269 (1986) 54 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    C. Appadu and T.J. Hollowood, /β-function of k-deformed AdS 5 × S 5string theory, JHEP11 (2015) 095 [arXiv:1507. 05420] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    B.C. Vallilo, One loop conformal invariance of the superstring in an AdS 5 × S 5background, JHEP12 (2002) 042 [hep-th/0210064] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  34. [34]
    N. Berkovits and P.S. Howe, Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys.B 635 (2002) 75 [hep-th/0112160] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    L. Mazzucato, Superstrings in AdS, Phys. Rept.521 (2012) 1 [arXiv:1104 .2604] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    N. Berkovits, Quantum consistency of the superstring in AdS 5 × S 5background, JHEP03 (2005) 041 [ hep-th/0411170] [INSPIRE].
  37. [37]
    O.A. Bedoya and O. Chandía, One-loop conformal invariance of the type II pure spinor superstring in a curved background, JHEP01 (2007) 042 [hep-th/0609161] [INSPIRE].MathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrasil
  2. 2.Departamento de FísicaUniversidade Federal de São CarlosSão CarlosBrasil

Personalised recommendations