Carrollian superstring in the flipped vacuum

TL;DR

This paper explores the spectrum and symmetries of Carrollian superstrings in the flipped vacuum, revealing their relation to BMS$_3$ symmetry, T-duality, and unique scattering amplitude features.

Contribution

It provides a detailed analysis of the Carrollian superstring spectrum, symmetry properties, and vertex operators, highlighting novel aspects of ultra-local Carrollian physics.

Findings

Carrollian superstrings share BMS$_3$ symmetry under T-duality.

Spectrum remains non-truncated with nonvanishing winding in flat background.

3-point amplitudes differ from tensile superstrings by a simple function.

Abstract

In this work, we study the spectrum of the Carrollian superstring in the flipped vacuum (the highest-weight representation) in detail. The target spacetime of the Carrollian string has a generalized Carrollian symmetry, and it is composed of both Poincar\'e directions and Carrollian directions. We explicitly show that two homogeneous Carrollian superstring theories, one with compactified Poincar\'e direction and the other with compactified Carrollian direction, share the same BMS$_3$ symmetry, and their zero modes can be identified under the usual T-duality transformation. Moreover, we investigate the spectrum of a general Carrollian superstring in the flipped vacuum. As the string can still have nonvanishing winding along the spatial direction in the infinite radius limit, the spectrum of the Carrollian strings in the flat background is no longer truncated. We furthermore construct the vertex operators of gravitons and discuss their scattering amplitudes. We find that the form of 3-point amplitudes differs from that of the usual tensile superstrings only by a simple function, which reflects the ultra-local nature of Carrollian physics.