( m, n )-string and D1-brane in stringy Newton-Cartan background
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Springer
Received: February 14, 2019 Accepted: April 18, 2019 Published: April 30, 2019
J. Klusoˇ n Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotl´ aˇrsk´ a 2, 611 37, Brno, Czech Republic
E-mail: [email protected] Abstract: This paper is devoted to the analysis of (m, n)-string in stringy Newton-Cartan background. We start with the Hamiltonian constraint for (m, n)-string in general background and perform limiting procedure on metric and NSNS and Ramond-Ramond two form background that leads to stringy Newton-Cartan gravity. We also analyze conditions that these background fields have to obey in order to define consistent world-sheet (m, n)−theory. We also discuss D1-brane with dynamical electric field in stringy NewtonCartan gravity. Keywords: D-branes, Bosonic Strings ArXiv ePrint: 1901.11292
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)163
JHEP04(2019)163
(m, n)-string and D1-brane in stringy Newton-Cartan background
Contents 1 Introduction
1
2 Hamiltonian formulation of D1-brane in general background
3
3 (m, n)-string in stringy NC background
4 8 11
5 D1-brane with unfixed gauge symmetry in NC background
12
6 Conclusion
14
1
Introduction
Recently new interesting generalization of Newton-Cartan (NC) gravity [1] was proposed in [2]. In standard NC gravity there is one-dimensional foliation direction of space-time corresponding to the absolute time direction that is longitudinal to the world-line of particle. The stringy NC gravity is generelization of this picture in the sense that one dimensional foliation is replaced by a two-dimensional foliation with one time-like and spatial foliation directions that are longitudinal to the world-sheet of the string. Further, stringy NC gravity is related to non-relativistic strings [3, 4] in the same way as general relativity is related to relativistic string theory as was recently discussed in [5].1 This paper also analyzed T-duality properties of non-relativistic strings in stringy Newton-Cartan background that are very interesting when it was shown that T-duality along the longitudinal direction of the stringy Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This fact was further confirmed in [9] when T-duality properties of non-relativistic string in stringy NC background was analyzed with the help of canonical formulation of this string sigma model found in [10]. Since the proposal suggested in [5] is very interesting we mean that it is natural to study further aspects of stringy NC. In particular, we would like to see whether it is possible to define another extended objects known in string theory, as for example D-branes [11] in this background. It is natural to begin with D1-brane which is two dimensional object with gauge field propagating on its world-sheet. This action couples to Ramond-Ramond (RR) two form and
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