Unstable D-brane in torsional Newton-Cartan background
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Springer
Received: February Revised: August Accepted: August Published: September
29, 11, 18, 30,
2020 2020 2020 2020
J. Klusoˇ n Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotl´ aˇrsk´ a 2, Brno 611 37, Czech Republic
E-mail: [email protected] Abstract: This paper is devoted to the construction of unstable D-brane action in torsional Newton-Cartan background through T-duality along null direction. We determine corresponding equations of motion and analyze their solution that corresponds to lower dimensional non-relativistic D(p-1)-brane. We also find Hamiltonian for unstable Dp-brane and study tachyon vacuum solutions that can be interpreted as gas of non-relativistic strings. Keywords: D-branes, Tachyon Condensation ArXiv ePrint: 2001.11543
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)191
JHEP09(2020)191
Unstable D-brane in torsional Newton-Cartan background
Contents 1 Introduction and summary
1
2 Non-relativistic unstable Dp-brane
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3 Tachyon kink solution
4
1
9 9 10
Introduction and summary
Newton Cartan (NC) gravity [1], which is covariant formulation of non-relativistic gravity, has been intensively studied in the past few years from different points of view. For example, torsionful generalization of NC geometry has an important place in the study of non-relativistic aspects of string theory and holography. Torsionful generalization NC which has non-exact clock form, was firstly observed as the boundary geometry in the context of Lifshitz holography [2–4]. There is also interesting relation between NC gravity and Hoˇrava-Lifshitz gravity [5] that was found in [6, 7]. Finally, there is also great interest in the analysis of non-relativistic string theory [9, 10] and its covariant version that was studied in [11–20]. At present there are two versions of non-relativistic string theories in NC background. The first one corresponds to strings on torsional NC background [12, 16, 20] which is basically defined as null reduction of relativistic string. The second one is known as stringy NC gravity [11, 13, 19] and it is defined as the special limit from relativistic string theory [11]. This limit can be considered as a generalization of the analysis presented [21] when the point particle probe is replaced by fundamental string. The beta function of the non-relativistic string in stringy NC background was determined in [17] that leads to the dynamical equations of corresponding stringy NC gravity. In case of torsional NC gravity the same result was derived in [18]. Then it was shown recently in [20] that these two non-relativistic string theories can be mapped each other. These results show that non-relativistic string theories are very important and certainly deserve further study. For example, in our previous paper [22] we introduced nonrelativistic D-branes in torsional NC background through dimensional reduction along null direction that can be interpreted as T-duality transformation of relativistic
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