The supersymmetric Neveu-Schwarz branes of non-relativistic string theory

Abstract

We construct the basic Neveu-Schwarz (NS) brane solutions of non-relativistic string theory using longitudinal T-duality as a solution generating technique. Extending the NS background fields to a supergravity multiplet, we verify that all solutions we find are half-supersymmetric. The two perturbative solutions we find both have an interpretation as the background geometry outside a string-like object. Correspondingly, we refer to these non-Lorentzian backgrounds as winding string and unwound string solution. Whereas the winding string is part of the on-shell spectrum of non-relativistic string theory, the unwound string only makes sense off-shell where it mediates the instantaneous gravitational force. Seen from the nine-dimensional point of view, we find that the winding string solution is sourced by a non-relativistic massive particle and that the unwound string solution is sourced by a massless Galilean particle of zero colour and spin. We explain how these two string solutions fit into a discrete lightcone quantization of string theory. We shortly discuss the basic NS five-brane and Kaluza-Klein monopole solutions and show that they are both half-supersymmetric.

Branched SL(2,ℤ) duality

“…Lately, effective field theories that arise from nonrelativistic string theory have been intensively studied, leading to novel nonrelativistic gravity and gauge theories [21][22][23][24][25][26][27][28][29][30][31][32][33] (for further references, see the review [34]). In [16,21], it is shown that the spacetime geometry underlying nonrelativistic closed string theory is non-Riemannian and has a codimensiontwo foliation structure.…”

“…it is natural to apply it together with the nonrelativistic T-duality transformations 16] to construct new half-BPS background solutions out of known solutions, such as a nonrelativistic version of the well-known D-brane solutions, along the lines of [33]. We expect that these solutions will provide an important input for a top-down construction of nonrelativistic holography.…”

Non-lorentzian supergravity and dualities

“…This observation does not come as a surprise since we do expect that the longitudinal T-duality relation extends beyond the purely bosonic structure to supergravity. This has been shown in more detail in [112,113]. Similarly, there is a natural relation between the additional fermionic S − /T −gauge symmetries in DSNC − supergravity and the fermionic part of the constraint multiplet.…”

“…The rules for the NSNS sector have previously been derived in [7] by performing a worldsheet duality along the lines of [47,111]. Here, we use the more direct approach of [112] to arrive at the same conclusion. The approach developed there is more in line with [110] and thus easily extendable to the Ramon-Ramond sector as we will show in subsection 5.3.4.…”

“…We are currently working on this in a separate project [70]. In the chapter, we follow our paper [112]. The basic idea presented here is to use the duality relation between Gomis-Ooguri string theory and the DLCQ of string theory to import knownledge from one side to the other.…”