On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins

TL;DR

This work analyzes the tensionless limit of bosonic strings in flat space by sending the string tension to zero (alpha' to infinity) while keeping oscillator variables fixed, revealing an infinite spectrum of massless higher-spin fields and a BRST structure that remains nilpotent in any dimension, thereby eliminating the conventional critical dimension. It uncovers an extensive symmetry algebra comprising spacetime Weyl symmetries and an internal sp(infty), organizing into g_O = w(1,dim-1) ⊕ sp(infty) and their universal enveloping real anti-Hermitian sector, and shows the closed string arises as a BRST-constrained subspace of the open theory. The tensionless limit of Witten's cubic string field theory indicates that interactions collapse to a zero-momentum sector acting only on oscillator zero-modes, yielding a matrix-model-like interacting sector while free dynamics persist for propagating degrees of freedom. These results align with expectations from higher-spin field theory on flat spacetime and motivate extensions to superstrings, curved backgrounds, and holographic contexts, with open questions about target-space interpretation, stability, and connections to Little String Theory and M-theory. Overall, the paper provides a concrete framework for tensionless string theories and their rich symmetry structure, offering a bridge between string theory and higher-spin approaches in a flat background.

Abstract

In the tensionless limit of string theory on flat background all the massive tower of states gets squeezed to a common zero mass level and the free theory is described by an infinite amount of massless free fields with arbitrary integer high spin. We notice that in this situation the very notion of critical dimension gets lost, the apparency of infinite global symmetries takes place, and the closed tensionless string can be realized as a constrained subsystem of the open one in a natural way. Moreover, we study the tensionless limit of the Witten's cubic sting field theory and find that the theory in such a limit can be represented as an infinite set of free arbitrary higher spin excitations plus an interacting sector involving their zero-modes only.