Abstract
We explore analytic integrability criteria for D1 branes probing 4D relativistic background with a null isometry direction. We use both the Kovacic’s algorithm of classical (non)integrability as well as the standard formulation of Lax connections to show the analytic integrability of the associated dynamical configuration. We further use the notion of double null reduction and obtain the world-volume action corresponding to a torsional Newton-Cartan (TNC) D0 brane probing a 3D torsional Newton-Cartan geometry. Moreover, following Kovacic’s method, we show the classical integrability of the TNC D0 brane configuration thus obtained. Finally, considering a trivial field redefinition for the D1 brane world-volume fields, we show the equivalence between two configurations in the presence of vanishing NS fluxes.
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References
J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys. 42 (2001) 3127 [hep-th/0009181] [INSPIRE].
J. Gomis and F. Passerini, Rotating solutions of non-relativistic string theory, Phys. Lett. B 617 (2005) 182 [hep-th/0411195] [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].
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].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic string theory and T-duality, JHEP 11 (2018) 133 [arXiv:1806.06071] [INSPIRE].
E.A. Bergshoeff, K.T. Grosvenor, C. Simsek and Z. Yan, An action for extended string Newton-Cartan gravity, JHEP 01 (2019) 178 [arXiv:1810.09387] [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].
D. Roychowdhury, Lax pairs for string Newton Cartan geometry, Nucl. Phys. B 954 (2020) 114990 [arXiv:1904.06485] [INSPIRE].
J. Gomis, J. Oh and Z. Yan, Nonrelativistic string theory in background fields, JHEP 10 (2019) 101 [arXiv:1905.07315] [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].
K.T. Grosvenor, J. Hartong, C. Keeler and N.A. Obers, Homogeneous nonrelativistic geometries as coset spaces, Class. Quant. Grav. 35 (2018) 175007 [arXiv:1712.03980] [INSPIRE].
M.H. Christensen, J. Hartong, N.A. Obers and B. Rollier, Torsional Newton-Cartan geometry and Lifshitz holography, Phys. Rev. D 89 (2014) 061901 [arXiv:1311.4794] [INSPIRE].
M.H. Christensen, J. Hartong, N.A. Obers and B. Rollier, Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography, JHEP 01 (2014) 057 [arXiv:1311.6471] [INSPIRE].
D. Roychowdhury, Nonrelativistic pulsating strings, JHEP 09 (2019) 002 [arXiv:1907.00584] [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].
A.D. Gallegos, U. Gürsoy and N. Zinnato, Torsional Newton Cartan gravity from non-relativistic strings, arXiv:1906.01607 [INSPIRE].
D. Roychowdhury, Nonrelativistic giant magnons from Newton Cartan strings, JHEP 02 (2020) 109 [arXiv:2001.01061] [INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS5 × S5 superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
C. Bachas and M. Petropoulos, Anti-de Sitter D-branes, JHEP 02 (2001) 025 [hep-th/0012234] [INSPIRE].
P.M. Petropoulos and S. Ribault, Some remarks on anti-de Sitter D-branes, JHEP 07 (2001) 036 [hep-th/0105252] [INSPIRE].
J.J. Kovacic, An algorithm for solving second order linear homogeneous differential equations, J. Symbol. Comput. 2 (1986) 3.
B.D. Saunders, An implementation of Kovacic’s algorithm for solving second order linear homogeneous differential equations, in Proceedings of the fourth ACM symposium on symbolic and algebraic computation — SYMSAC ′ 81, ACM press, U.S.A. (1981), pg. 105.
P. Basu and L.A. Pando Zayas, Analytic non-integrability in string theory, Phys. Rev. D 84 (2011) 046006 [arXiv:1105.2540] [INSPIRE].
A. Stepanchuk and A.A. Tseytlin, On (non)integrability of classical strings in p-brane backgrounds, J. Phys. A 46 (2013) 125401 [arXiv:1211.3727] [INSPIRE].
D. Giataganas, L.A. Pando Zayas and K. Zoubos, On marginal deformations and non-integrability, JHEP 01 (2014) 129 [arXiv:1311.3241] [INSPIRE].
D. Giataganas and K. Sfetsos, Non-integrability in non-relativistic theories, JHEP 06 (2014) 018 [arXiv:1403.2703] [INSPIRE].
Y. Chervonyi and O. Lunin, (Non)-integrability of geodesics in D-brane backgrounds, JHEP 02 (2014) 061 [arXiv:1311.1521] [INSPIRE].
D. Roychowdhury, Analytic integrability for strings on η and λ deformed backgrounds, JHEP 10 (2017) 056 [arXiv:1707.07172] [INSPIRE].
C. Núñez, D. Roychowdhury and D.C. Thompson, Integrability and non-integrability in N = 2 SCFTs and their holographic backgrounds, JHEP 07 (2018) 044 [arXiv:1804.08621] [INSPIRE].
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Roychowdhury, D. Newton-Cartan D0 branes from D1 branes and integrability. J. High Energ. Phys. 2020, 120 (2020). https://doi.org/10.1007/JHEP06(2020)120
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DOI: https://doi.org/10.1007/JHEP06(2020)120