Abstract
We investigate how SL(2,ℤ) duality is realized in nonrelativistic type IIB superstring theory, which is a self-contained corner of relativistic string theory. Within this corner, we realize manifestly SL(2,ℤ)-invariant (p, q)-string actions. The construction of these actions imposes a branching between strings of opposite charges associated with the two-form fields. The branch point is determined by these charges and the axion background field. Both branches must be incorporated in order to realize the full SL(2,ℤ) group. Besides these string actions, we also construct D-instanton and D3-brane actions that manifestly realize the branched SL(2,ℤ) symmetry.
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References
J.H. Schwarz and P.C. West, Symmetries and Transformations of Chiral N = 2 D = 10 Supergravity, Phys. Lett. B 126 (1983) 301 [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
J.H. Schwarz, An SL(2,Z) multiplet of type IIB superstrings, Phys. Lett. B 360 (1995) 13 [Erratum ibid. 364 (1995) 252] [hep-th/9508143] [INSPIRE].
K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press (12, 2006), https://doi.org/10.1017/CBO9780511816086 [INSPIRE].
J.L. Cardy, Duality and the Theta Parameter in Abelian Lattice Models, Nucl. Phys. B 205 (1982) 17 [INSPIRE].
J.L. Cardy and E. Rabinovici, Phase Structure of Z(p) Models in the Presence of a Theta Parameter, Nucl. Phys. B 205 (1982) 1 [INSPIRE].
A.D. Shapere and F. Wilczek, Selfdual Models with Theta Terms, Nucl. Phys. B 320 (1989) 669 [INSPIRE].
P.K. Townsend, Membrane tension and manifest IIB S duality, Phys. Lett. B 409 (1997) 131 [hep-th/9705160] [INSPIRE].
M. Cederwall and P.K. Townsend, The Manifestly Sl(2,Z) covariant superstring, JHEP 09 (1997) 003 [hep-th/9709002] [INSPIRE].
A.A. Tseytlin, Selfduality of Born-Infeld action and Dirichlet three-brane of type IIB superstring theory, Nucl. Phys. B 469 (1996) 51 [hep-th/9602064] [INSPIRE].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, SL(2,R)-invariant IIB Brane Actions, JHEP 02 (2007) 007 [hep-th/0611036] [INSPIRE].
I.R. Klebanov and J.M. Maldacena, (1+1)-dimensional NCOS and its U(N) gauge theory dual, Adv. Theor. Math. Phys. 4 (2000) 283 [hep-th/0006085] [INSPIRE].
J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys. 42 (2001) 3127 [hep-th/0009181] [INSPIRE].
U.H. Danielsson, A. Guijosa and M. Kruczenski, IIA/B, wound and wrapped, JHEP 10 (2000) 020 [hep-th/0009182] [INSPIRE].
S. Ebert, H.-Y. Sun and Z. Yan, Dual D-brane actions in nonrelativistic string theory, JHEP 04 (2022) 161 [arXiv:2112.09316] [INSPIRE].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-duality, JHEP 11 (2018) 133 [arXiv:1806.06071] [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
L. Susskind, Another conjecture about M(atrix) theory, hep-th/9704080 [INSPIRE].
N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009] [INSPIRE].
A. Sen, D0-branes on Tn and matrix theory, Adv. Theor. Math. Phys. 2 (1998) 51 [hep-th/9709220] [INSPIRE].
R. Andringa, E. Bergshoeff, J. Gomis and M. de Roo, ’Stringy’ Newton-Cartan Gravity, Class. Quant. Grav. 29 (2012) 235020 [arXiv:1206.5176] [INSPIRE].
T. Harmark, J. Hartong and N.A. Obers, Nonrelativistic strings and limits of the AdS/CFT correspondence, Phys. Rev. D 96 (2017) 086019 [arXiv:1705.03535] [INSPIRE].
T. Harmark, J. Hartong, L. Menculini, N.A. Obers and Z. Yan, Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence, JHEP 11 (2018) 190 [arXiv:1810.05560] [INSPIRE].
T. Harmark, J. Hartong, L. Menculini, N.A. Obers and G. Oling, Relating non-relativistic string theories, JHEP 11 (2019) 071 [arXiv:1907.01663] [INSPIRE].
E.A. Bergshoeff, J. Gomis, J. Rosseel, C. Şimşek and Z. Yan, String Theory and String Newton-Cartan Geometry, J. Phys. A 53 (2020) 014001 [arXiv:1907.10668] [INSPIRE].
J. Klusoň, (m, n)-String and D1-Brane in Stringy Newton-Cartan Background, JHEP 04 (2019) 163 [arXiv:1901.11292] [INSPIRE].
J. Klusoň, Non-Relativistic D-brane from T-duality Along Null Direction, JHEP 10 (2019) 153 [arXiv:1907.05662] [INSPIRE].
A.D. Gallegos, U. Gürsoy, S. Verma and N. Zinnato, Non-Riemannian gravity actions from double field theory, JHEP 06 (2021) 173 [arXiv:2012.07765] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, Nonrelativistic Open String and Yang-Mills Theory, JHEP 03 (2021) 269 [arXiv:2007.01886] [INSPIRE].
E.A. Bergshoeff, J. Lahnsteiner, L. Romano, J. Rosseel and C. Şimşek, A non-relativistic limit of NS-NS gravity, JHEP 06 (2021) 021 [arXiv:2102.06974] [INSPIRE].
L. Bidussi, T. Harmark, J. Hartong, N.A. Obers and G. Oling, Torsional string Newton-Cartan geometry for non-relativistic strings, JHEP 02 (2022) 116 [arXiv:2107.00642] [INSPIRE].
E.A. Bergshoeff, J. Lahnsteiner, L. Romano, J. Rosseel and C. Simsek, Non-relativistic ten-dimensional minimal supergravity, JHEP 12 (2021) 123 [arXiv:2107.14636] [INSPIRE].
E. Bergshoeff, J. Lahnsteiner, L. Romano and J. Rosseel, The supersymmetric Neveu-Schwarz branes of non-relativistic string theory, JHEP 08 (2022) 218 [arXiv:2204.04089] [INSPIRE].
G. Oling and Z. Yan, Aspects of Nonrelativistic Strings, Front. in Phys. 10 (2022) 832271 [arXiv:2202.12698] [INSPIRE].
J. Gomis, J. Oh and Z. Yan, Nonrelativistic String Theory in Background Fields, JHEP 10 (2019) 101 [arXiv:1905.07315] [INSPIRE].
A.D. Gallegos, U. Gürsoy and N. Zinnato, Torsional Newton Cartan gravity from non-relativistic strings, JHEP 09 (2020) 172 [arXiv:1906.01607] [INSPIRE].
Z. Yan and M. Yu, Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory, JHEP 03 (2020) 181 [arXiv:1912.03181] [INSPIRE].
Z. Yan, Torsional deformation of nonrelativistic string theory, JHEP 09 (2021) 035 [arXiv:2106.10021] [INSPIRE].
R. Gopakumar, J.M. Maldacena, S. Minwalla and A. Strominger, S duality and noncommutative gauge theory, JHEP 06 (2000) 036 [hep-th/0005048] [INSPIRE].
J. Gomis, Z. Yan and M. Yu, T-duality in Nonrelativistic Open String Theory, JHEP 02 (2021) 087 [arXiv:2008.05493] [INSPIRE].
J.G. Russo and M.M. Sheikh-Jabbari, On noncommutative open string theories, JHEP 07 (2000) 052 [hep-th/0006202] [INSPIRE].
R.-G. Cai and N. Ohta, (F1, D1, D3) bound state, its scaling limits and SL(2,Z) duality, Prog. Theor. Phys. 104 (2000) 1073 [hep-th/0007106] [INSPIRE].
J.X. Lu, S. Roy and H. Singh, SL(2, Z) duality and four-dimensional noncommutative theories, Nucl. Phys. B 595 (2001) 298 [hep-th/0007168] [INSPIRE].
U. Gran and M. Nielsen, Noncommutative open (p,q) string theories, JHEP 11 (2001) 022 [hep-th/0104168] [INSPIRE].
J. Gomis, J. Gomis and K. Kamimura, Non-relativistic superstrings: A New soluble sector of AdS5 × S5, JHEP 12 (2005) 024 [hep-th/0507036] [INSPIRE].
U.H. Danielsson, A. Guijosa and M. Kruczenski, Newtonian gravitons and D-brane collective coordinates in wound string theory, JHEP 03 (2001) 041 [hep-th/0012183] [INSPIRE].
Z. Yan and M. Yu, KLT factorization of nonrelativistic string amplitudes, JHEP 04 (2022) 068 [arXiv:2112.00025] [INSPIRE].
P.K. Townsend, Four lectures on M-theory, in ICTP Summer School in High-energy Physics and Cosmology, pp. 385–438, 12, 1996 [hep-th/9612121] [INSPIRE].
M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, Dual D-brane actions, Nucl. Phys. B 496 (1997) 215 [hep-th/9702133] [INSPIRE].
A. Dabholkar and J.A. Harvey, Nonrenormalization of the Superstring Tension, Phys. Rev. Lett. 63 (1989) 478 [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
S.S. Gubser, S. Gukov, I.R. Klebanov, M. Rangamani and E. Witten, The Hagedorn transition in noncommutative open string theory, J. Math. Phys. 42 (2001) 2749 [hep-th/0009140] [INSPIRE].
P. Meessen and T. Ortín, An Sl(2,Z) multiplet of nine-dimensional type-II supergravity theories, Nucl. Phys. B 541 (1999) 195 [hep-th/9806120] [INSPIRE].
J. Gomis, K. Kamimura and P.K. Townsend, Non-relativistic superbranes, JHEP 11 (2004) 051 [hep-th/0409219] [INSPIRE].
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Bergshoeff, E.A., Grosvenor, K.T., Lahnsteiner, J. et al. Branched SL(2,ℤ) duality. J. High Energ. Phys. 2022, 131 (2022). https://doi.org/10.1007/JHEP10(2022)131
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DOI: https://doi.org/10.1007/JHEP10(2022)131