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

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.

Latex, 12p

References in corpus (5)

• Generalized Duality and Singular Strings in Higher Dimensions
• Conservation Laws and Geometry of Perturbed Coset Models
• W-Geometries
• Classical A_n--W-Geometry
• Target Space Description of W-Infinity Symmetry in Coset Models

Cited by in corpus (6)

• Conservation Laws and Geometry of Perturbed Coset Models
• Universal aspects of string propagation on curved backgrounds
• An Infinite Dimensional Symmetry Algebra in String Theory
• Minimal surfaces in AdS space and Integrable systems
• The branch process of the cosmic strings
• Categorical Foundation of Quantum Mechanics and String Theory