The Tensionless Lives of Null Strings

Abstract: The tensionless limit probes the very high energy regime of string theory in contrast to the well studied point-particle limit which reduces to Einstein gravity. Tensionless strings sweep out null worldsheets in the target space and hence are also called null strings. This article aims to provide a comprehensive review of tensionless null string theory beginning with the initial work of Schild, and continuing to the foundational work of Isberg et al (ILST) and then focussing on developments in the past decade. Recent work centres on the emergence of the Carrollian Conformal Algebra as residual worldsheet symmetries of the ILST action and the identification of tensionless limit as a worldsheet Carrollian limit on the string worldsheet. Carrollian structures are used to address the classical and quantum aspects of the null string. In the classical theory, the aforementioned limit agrees with the analysis from the ILST action. Symmetries, constraints, mode expansions computed from both perspectives match nicely providing a robust cross-check of the analyses. We discuss closed and open null strings as well as their supersymmetric cousins. The quantum null string comes with several surprises, the foremost of which is the emergence of three consistent quantum theories from the ILST action. We detail the canonical quantisation and the spectrum of the triumvirate of theories. We discuss the novelties of the quantum null theories and the effect compactifaction has on them. We also discuss Carroll strings, applications of these ideas to strings approaching black holes and give a quick overview of other related developments.