Longitudinal Galilean and Carrollian limits of non-relativistic strings

Starting from the Polyakov action we consider two distinct Carroll limits in target space, keeping the string worldsheet relativistic. The resulting magnetic and chiral Carroll string models exhibit different symmetries and dynamics. Both models have an infinite dimensional symmetry algebra with Carroll symmetry included in a finite dimensional subalgebra. For the magnetic model, this is the so-called string Carroll algebra. The chiral model realises an extended version of the string Carroll algebra. The magnetic model does not have any transverse string excitations. The chiral model is less restrictive and includes arbitrary left-moving modes that carry transverse momentum but do not contribute to the energy in target space.

Carroll strings with an extended symmetry algebra

Harksen,

Hidalgo,

Sybesma

et al. 2024

Worldsheet formalism for decoupling limits in string theory

Gomis,

Yan

2024

We study the bosonic sector of a decoupling limit of type IIA superstring theory, where a background Ramond-Ramond one-form is fined tuned to its critical value, such that it cancels the associated background D0-brane tension. The light excitations in this critical limit are D0-branes, whose dynamics is described by the Banks-Fischler-Shenker-Susskind (BFSS) Matrix theory that corresponds to M-theory in the Discrete Light-Cone Quantization (DLCQ). We develop the worldsheet formalism for the fundamental string in the same critical limit of type IIA superstring theory. We show that the fundamental string develops singularities on its worldsheet, whose topology is described by nodal Riemann spheres as in ambitwistor string theory. We study the T-duality transformations of this string sigma model and provide a worldsheet derivation for the recently revived and expanded duality web that unifies a zoo of decoupling limits in type II superstring theories. By matching the string worldsheet actions, we demonstrate how some of these decoupling limits are related to tensionless (and ambitwistor) string theory, Carrollian string theory, the Spin Matrix limits of the AdS/CFT correspondence, and more.

Non-relativistic expansion of open strings and D-branes

Hartong,

Have

2024

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].