W-Infinity Symmetry of the Nambu-Goto String in 4 Dimensions

TL;DR

This paper reveals a hidden $W_{}$ symmetry in the classical bosonic string in 4D Minkowski space, connecting its transverse modes to an $SU(2)/U(1)$ coset model and proposing generalizations and transformations related to Liouville theories.

Contribution

It uncovers a hidden $W_{}$ symmetry in the classical string and links it to coset models and Liouville-like transformations, offering new insights into string symmetries.

Findings

Identification of $W_{}$ symmetry in the classical string

Equivalence of transverse modes with $SU(2)/U(1)$ coset model

Proposal of a Liouville-like transformation connecting solutions

Abstract

We consider a bosonic string propagating in 4--dim Minkowski space. We show that in the orthonormal gauge the classical system exhibits a hidden $W_{\infty}$ chiral symmetry, arising from the equivalence of its transverse modes with the $SU(2)/U(1)$ coset model defined on the string world--sheet. Generalizations to other string backgrounds are proposed. We also define a Liouville--like transformation that maps solutions of the $SU(2)/U(1)$ coset model into the solution space of two decoupled Liouville theories. Inverting this transformation, however, remains an open problem.