Tensionless Strings and Galilean Conformal Algebra

TL;DR

This work shows that the tensionless limit of closed bosonic strings naturally realizes the 2d Galilean Conformal Algebra as the residual worldsheet symmetry in a conformal-gauge-like setting, with the limit described by an ultra-relativistic contraction of the parent Virasoro algebras. It develops the GCFT energy-momentum structure, discusses central charges and the lack of a fixed critical dimension in the simplest tensionless regime, and demonstrates a dual NR contraction whose Cardy-like state counting matches that of the UR frame on a torus. A central result is the equivalence of the two contractions in a torus setting and the proposed duality between tensionless (UR) and point-particle–like (NR) limits, enabling a structured approach to the tensionless spectrum via $2d$ GCFT tools. The findings illuminate potential pathways to flat-space holography, linking GCFT symmetries to BMS$_3$, and lay out multiple future directions, including extensions to open strings, supersymmetry, BRST quantization, and higher-spin holography in tensionless regimes.

Abstract

We find an intriguing link between the symmetries of the tensionless limit of closed string theory and the 2-dimensional Galilean Conformal Algebra (2d GCA). 2d GCA has been discussed in the context of the non-relativistic limit of AdS/CFT and more recently in flat-space holography as the proposed symmetry algebra of the field theory dual to 3d Minkowski spacetimes. It is best understood as a contraction of two copies of the Virasoro algebra. In this note, we link this to the tensionless limit of bosonic closed string theory. We show how it emerges naturally as a contraction of the residual gauge symmetries of the tensile string in the conformal gauge. We also discuss a possible "dual" interpretation in terms of a point-particle like limit.