On Tensionless Strings in $3+1$ Dimensions

TL;DR

This paper demonstrates the existence of tensionless strings in 3+1 dimensions using an M-theory construction with two intersecting 5-branes connected by a 2-brane, whose boundary becomes a tensionless string as the branes coincide. It shows that the massless spectrum of the resulting theory lacks a graviton and comprises a $N=2$ vector multiplet alongside charged matter, consistent with the 3+1D Green-Schwarz string; the dynamics are explored both in a low-energy field-theory framework (including a Meissner-like phase and Nielsen-Olesen vortices) and in a gravitational context via near-extremal entropy, which can be interpreted as a gas of effective strings on the intersection. The results suggest two realizations of tensionless strings in 3+1D: (i) boundaries of stretched membranes between coincident 5-branes, and (ii) 5-branes wrapped on $T^4$, with the tension tunable to approach zero. Collectively, the findings provide a concrete, gravity-decoupled string-theoretic sector in M-theory and link these tensionless strings to lower-dimensional gauge theories through compactification, offering insights into non-critical string dynamics and potential extensions to non-abelian setups.

Abstract

We argue for the existence of phase transitions in $3+1$ dimensions associated with the appearance of tensionless strings. The massless spectrum of this theory does not contain a graviton: it consists of one $N=2$ vector multiplet and one linear multiplet, in agreement with the light-cone analysis of the Green-Schwarz string in $3+1$ dimensions. In M-theory the string decoupled from gravity arises when two 5-branes intersect over a three-dimensional hyperplane. The two 5-branes may be connected by a 2-brane, whose boundary becomes a tensionless string with $N=2$ supersymmetry in $3+1$ dimensions. Non-critical strings on the intersection may also come from dynamical 5-branes intersecting the two 5-branes over a string and wrapped over a four-torus. The near-extremal entropy of the intersecting 5-branes is explained by the non-critical strings originating from the wrapped 5-branes.