Non-relativistic intersecting branes, Newton-Cartan geometry and AdS/CFT

We expand the relativistic open bosonic string in powers of 1/c2 where c is the speed of light. We perform this expansion to next-to-leading order in 1/c2 and relate our results to known descriptions of non-relativistic open strings obtained by taking limits. Just as for closed strings the non-relativistic expansion is well-defined if the open string winds a circle in the target space. This direction must satisfy Dirichlet boundary conditions. It is shown that the endpoints of the open string behave as Bargmann particles in the non-relativistic regime. These open strings end on nrDp-branes with p ≤ 24. When these nrDp-branes do not fluctuate they correspond to (p + 1)-dimensional Newton-Cartan submanifolds of the target space. When we include fluctuations and worldvolume gauge fields their dynamics is described by a non-relativistic version of the DBI action whose form we derive from symmetry considerations. The worldvolume gauge field and scalar field of a nrD24-brane make up the field content of Galilean electrodynamics (GED), and the effective theory on the nrD24-brane is precisely a non-linear version of GED. We generalise these results to actions for any nrDp-brane by demanding that they have the same target space gauge symmetries that the non-relativistic open and closed string actions have. Finally, we show that the nrDp-brane action is transverse T-duality covariant. Our results agree with the findings of Gomis, Yan and Yu in [1].

Non-relativistic expansion of open strings and D-branes

Hartong,

Have

2024

The surprising structure of non-relativistic 11-dimensional supergravity

Bergshoeff,

Blair,

Lahnsteiner

et al. 2024

We study a non-relativistic limit of 11-dimensional supergravity. This limit leads to a theory with an underlying membrane Newton-Cartan geometry. Consistency of the non-relativistic limit requires the imposition of constraints, requiring that certain bosonic and fermionic torsions and curvatures vanish. We investigate the implications of two versions of these constraints. In one version, we keep only 16 supersymmetry transformations, leading to a simple (purely bosonic) constraint structure but an unusual realisation of the supersymmetry algebra which does not close into diffeomorphisms. In the other, we keep all 32 supersymmetry transformations. This requires a complicated sequence of bosonic and fermionic constraints, eventually involving three derivatives of bosonic fields. We argue, with a linearised calculation, that this sequence of constraints terminates. Furthermore, we show that there exists a family of supersymmetric solutions satisfying these constraints, containing the non-relativistic limit of the M2 supergravity solution recently obtained by Lambert and Smith as a background relevant for non-relativistic holography.

Reciprocal non-relativistic decoupling limits of String Theory and M-Theory

Lambert,

Smith

2024

It has recently been realised that there are supersymmetry-preserving non-relativistic decoupling limits associated with each half-BPS object in String Theory and M-Theory. We argue that, given a p-brane and a q-brane for which there is a quarter-BPS intersecting configuration, the p-brane decoupling limit of the q-brane’s worldvolume QFT is necessarily equal to the reciprocal q-brane decoupling limit of the p-brane’s worldvolume theory. This is explicitly shown for the cases of the D0-D4 and D1-D3 systems. As an application of this idea, we use the reciprocal pair of limits in the M2-M5 system to describe the dynamics of interacting self-dual strings in the six-dimensional $$ \mathcal{N} $$ N = (2, 0) theory. We also discuss the limits of the dual gravitational theories and, using symmetries, argue that the duality is maintained by the limits.