Advertisement

\( T\overline{T} \)-deformed actions and (1,1) supersymmetry

  • Evan A. ColemanEmail author
  • Jeremias Aguilera-Damia
  • Daniel Z. Freedman
  • Ronak M. Soni
Regular Article - Theoretical Physics

Abstract

We describe an algorithmic method to calculate the \( T\overline{T} \) deformed Lagrangian of a given seed theory by solving an algebraic system of equations. This method is derived from the topological gravity formulation of the deformation. This algorithm is far simpler than the direct partial differential equations needed in most earlier proposals. We present several examples, including the deformed Lagrangian of (1,1) supersymmetry. We show that this Lagrangian is off-shell invariant through order λ2 in the deformation parameter and verify its SUSY algebra through order λ.

Keywords

Field Theories in Lower Dimensions Sigma Models Topological Field Theories 

Supplementary material

13130_2019_11393_MOESM1_ESM.nb (87 kb)
ESM 1 (NB 87 kb)

References

  1. [1]
    A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \)in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
  2. [2]
    F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys.B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    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].
  4. [4]
    G. Bonelli, N. Doroud and M. Zhu, \( T\overline{T} \) -deformations in closed form, JHEP06 (2018) 149 [arXiv:1804.10967] [INSPIRE].
  5. [5]
    M. Baggio, A. Sfondrini, G. Tartaglino-Mazzucchelli and H. Walsh, On \( T\overline{T} \)deformations and supersymmetry, JHEP06 (2019) 063 [arXiv:1811.00533] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    C.-K. Chang, C. Ferko and S. Sethi, Supersymmetry and \( T\overline{T} \)deformations, JHEP04 (2019) 131 [arXiv:1811.01895] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S. Frolov, \( T\overline{T} \)deformation and the light-cone gauge, arXiv:1905.07946 [INSPIRE].
  8. [8]
    R. Conti, L. Iannella, S. Negro and R. Tateo, Generalised Born-Infeld models, Lax operators and the \( T\overline{T} \)perturbation, JHEP11 (2018) 007 [arXiv:1806.11515] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2holography and \( T\overline{T} \), JHEP09 (2017) 136 [arXiv:1706.06604] [INSPIRE].ADSCrossRefGoogle Scholar
  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].ADSCrossRefGoogle Scholar
  11. [11]
    J. Cardy, The \( T\overline{T} \)deformation of quantum field theory as random geometry, JHEP10 (2018) 186 [arXiv:1801.06895] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    R. Conti, S. Negro and R. Tateo, The \( T\overline{T} \)perturbation and its geometric interpretation, JHEP02 (2019) 085 [arXiv:1809.09593] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    R. Conti, S. Negro and R. Tateo, Conserved currents and \( T{\overline{T}}_s \)irrelevant deformations of 2D integrable field theories, arXiv:1904.09141 [INSPIRE].
  14. [14]
    V. Gorbenko, \( T\overline{T} \)as simple gravity, talk given at \( T\overline{T} \)and other solvable deformations of quantum field theories, April 8-12, Simons Centre for Geometry and Physics, Stony Brook, U.S.A. (2019).Google Scholar
  15. [15]
    L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
  16. [16]
    J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2007).Google Scholar
  17. [17]
    H. Jiang, A. Sfondrini and G. Tartaglino-Mazzucchelli, \( T\overline{T} \) deformations with \( \mathcal{N} \) = (0, 2) supersymmetry, Phys. Rev. D 100 (2019) 046017 [arXiv:1904.04760] [INSPIRE].
  18. [18]
    C.-K. Chang et al., \( T\overline{T} \)Flows and (2,2) Supersymmetry, arXiv:1906.00467 [INSPIRE].
  19. [19]
    S. Dubovsky, Beyond \( T\overline{T} \), talk given at \( T\overline{T} \)and other solvable deformations of quantum field theories, April 8-12, Simons Centre for Geometry and Physics, Stony Brook, U.S.A. (2019).Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Stanford Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanfordU.S.A.
  2. 2.Centro Atómico Bariloche and CONICETBarilocheArgentina
  3. 3.Center for Theoretical Physics and Department of MathematicsMassachusetts Institute of TechnologyCambridgeU.S.A.

Personalised recommendations