(Anti-)De Sitter null strings and Carroll-Weyl symmetry

Abstract

We construct a $d{S}_d$ null string in a novel way by lifting the standard tensionless string to $R^{1,d}$. Gauging worldsheet scale symmetry introduces terms in the action breaking translation invariance, but preserving the $d{S}_d$ symmetry $SO(1,d)$. Choosing a De Sitter symmetric gauge fixing of the scale symmetry yields a $d$ dimensional theory which we show has all the expected properties of $d{S}_d$ tensionless strings. The action happens to be the intriguing Carrol-Weyl symmetric string action in $R^{1,d}$, now with a clear target space interpretation in $d$ dimensions. That it does not, as recently claimed, represent a ($d+1$)-dimensional string in flat ($d+1$)-dimensional Minkowski space settles an apparent issue with the Carrol-Weyl string model. Furthermore, while there are clear obstacles for similar formulations of tensile strings in (A)dS backgrounds, our new insights are easily modified to the formulation of Anti-De Sitter tensionless strings. That our construction generates a curved geometry purely algebraically may have even wider applications.

8 pages, no figures