Abstract
We explore the J \( \overline{T} \) and T \( \overline{J} \) deformations of two-dimensional field theories possessing \( \mathcal{N} \) = (0, 1), (1, 1) and (0, 2) supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the J \( \overline{T} \)/T \( \overline{J} \) deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional J \( \overline{T} \)/T \( \overline{J} \) operator on-shell. We also present some examples of J \( \overline{T} \)/T \( \overline{J} \) flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.
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References
A.B. Zamolodchikov, Expectation value of composite field T \( \overline{T} \)in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, T \( \overline{T} \)-deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
Y. Jiang, Lectures on solvable irrelevant deformations of 2d quantum field theory, arXiv:1904.13376 [INSPIRE].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys. 5 (2018) 048 [arXiv:1710.08415] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, T \( \overline{T} \), J \( \overline{T} \), T \( \overline{T} \)and String Theory, J. Phys. A 52 (2019) 384003 [arXiv:1905.00051] [INSPIRE].
A. Bzowski and M. Guica, The holographic interpretation of J \( \overline{T} \)-deformed CFTs, JHEP 01 (2019) 198 [arXiv:1803.09753] [INSPIRE].
Y. Nakayama, Holographic dual of conformal field theories with very special T \( \overline{J} \)deformations, Phys. Rev. D 100 (2019) 086011 [arXiv:1905.05353] [INSPIRE].
J. Aguilera-Damia, V.I. Giraldo-Rivera, E.A. Mazenc, I. Salazar Landea and R.M. Soni, A Path Integral Realization of Joint J \( \overline{T} \), T \( \overline{J} \)and T \( \overline{T} \)Flows, arXiv:1910.06675 [INSPIRE].
T. Anous and M. Guica, A general definition of J Ta -deformed QFTs, arXiv:1911.02031 [INSPIRE].
O. Aharony, S. Datta, A. Giveon, Y. Jiang and D. Kutasov, Modular covariance and uniqueness of J \( \overline{T} \)deformed CFTs, JHEP 01 (2019) 085 [arXiv:1808.08978] [INSPIRE].
M. Guica, On correlation functions in J \( \overline{T} \)-deformed CFTs, J. Phys. A 52 (2019) 184003 [arXiv:1902.01434] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, J \( \overline{T} \)deformed CFT2 and string theory, JHEP 10 (2018) 057 [arXiv:1806.09667] [INSPIRE].
L. Apolo and W. Song, Strings on warped AdS3 via T\( \overline{\mathrm{J}} \)deformations, JHEP 10 (2018) 165 [arXiv:1806.10127] [INSPIRE].
Y. Nakayama, Very Special T \( \overline{J} \)deformed CFT, Phys. Rev. D 99 (2019) 085008 [arXiv:1811.02173] [INSPIRE].
T. Araujo, E. Colgáin, Y. Sakatani, M.M. Sheikh-Jabbari and H. Yavartanoo, Holographic integration of T \( \overline{T} \) & J \( \overline{T} \)via O(d, d), JHEP 03 (2019) 168 [arXiv:1811.03050] [INSPIRE].
A. Giveon, Comments on T \( \overline{T} \), J \( \overline{T} \)and String Theory, arXiv:1903.06883 [INSPIRE].
R. Conti, S. Negro and R. Tateo, Conserved currents and T\( \overline{T} \)s irrelevant deformations of 2D integrable field theories, JHEP 11 (2019) 120 [arXiv:1904.09141] [INSPIRE].
L. Apolo and W. Song, Heating up holography for single-trace J \( \overline{T} \)deformations, JHEP 01 (2020) 141 [arXiv:1907.03745] [INSPIRE].
A. Hashimoto and D. Kutasov, T \( \overline{T} \), J \( \overline{T} \), T \( \overline{J} \)partition sums from string theory, JHEP 02 (2020) 080 [arXiv:1907.07221] [INSPIRE].
S. He and H. Shu, Correlation functions, entanglement and chaos in the T \( \overline{T} \)/J \( \overline{T} \)-deformed CFTs, JHEP 02 (2020) 088 [arXiv:1907.12603] [INSPIRE].
T.R. Araujo, Nonlocal charges from marginal deformations of 2D CFTs: Holographic T \( \overline{T} \)and T \( \overline{J} \)and Yang-Baxter deformations, Phys. Rev. D 101 (2020) 025008 [arXiv:1909.08149] [INSPIRE].
S. Frolov, T \( \overline{T} \), \( \tilde{J} \)J , J T and \( \tilde{J} \)T deformations, J. Phys. A 53 (2020) 025401 [arXiv:1907.12117] [INSPIRE].
C.-K. Chang, C. Ferko and S. Sethi, Supersymmetry and T \( \overline{T} \)deformations, JHEP 04 (2019) 131 [arXiv:1811.01895] [INSPIRE].
M. Baggio, A. Sfondrini, G. Tartaglino-Mazzucchelli and H. Walsh, On T \( \overline{T} \)deformations and supersymmetry, JHEP 06 (2019) 063 [arXiv:1811.00533] [INSPIRE].
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].
C.-K. Chang, C. Ferko, S. Sethi, A. Sfondrini and G. Tartaglino-Mazzucchelli, T \( \overline{T} \)flows and (2, 2) supersymmetry, Phys. Rev. D 101 (2020) 026008 [arXiv:1906.00467] [INSPIRE].
C. Ferko, H. Jiang, S. Sethi and G. Tartaglino-Mazzucchelli, Non-linear supersymmetry and T \( \overline{T} \)-like flows, JHEP 02 (2020) 016 [arXiv:1910.01599] [INSPIRE].
E.A. Coleman, J. Aguilera-Damia, D.Z. Freedman and R.M. Soni, T \( \overline{T} \)-deformed actions and (1, 1) supersymmetry, JHEP 10 (2019) 080 [arXiv:1906.05439] [INSPIRE].
G. Bonelli, N. Doroud and M. Zhu, T \( \overline{T} \)-deformations in closed form, JHEP 06 (2018) 149 [arXiv:1804.10967] [INSPIRE].
R. Brooks and S.J. Gates, Jr., Unidexterous D = 2 supersymmetry in superspace. 2. Quantization, Phys. Lett. B 184 (1987) 217 [INSPIRE].
T.T. Dumitrescu and N. Seiberg, Supercurrents and Brane Currents in Diverse Dimensions, JHEP 07 (2011) 095 [arXiv:1106.0031] [INSPIRE].
J. Hughes and J. Polchinski, Partially Broken Global Supersymmetry and the Superstring, Nucl. Phys. B 278 (1986) 147 [INSPIRE].
A. Smailagic and E. Spallucci, General treatment of anomalies in (1, 0) and (1, 1) two-dimensional supergravity, Class. Quant. Grav. 10 (1993) 451 [hep-th/9212142] [INSPIRE].
J. Cardy, T \( \overline{T} \)deformations of non-Lorentz invariant field theories, arXiv:1809.07849 [INSPIRE].
S.J. Gates, Jr., M.T. Grisaru, L. Mezincescu and P.K. Townsend, (1, 0) supergraphity, Nucl. Phys. B 286 (1987) 1 [INSPIRE].
S. Ferrara, Supersymmetric Gauge Theories in Two-Dimensions, Lett. Nuovo Cim. 13 (1975) 629 [INSPIRE].
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Jiang, H., Tartaglino-Mazzucchelli, G. Supersymmetric J \( \overline{T} \) and T \( \overline{J} \) deformations. J. High Energ. Phys. 2020, 140 (2020). https://doi.org/10.1007/JHEP05(2020)140
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DOI: https://doi.org/10.1007/JHEP05(2020)140