An Infinite Dimensional Symmetry Algebra in String Theory

Abstract

Symmetry transformations of the space-time fields of string theory are generated by certain similarity transformations of the stress-tensor of the associated conformal field theories. This observation is complicated by the fact that, as we explain, many of the operators we habitually use in string theory (such as vertices and currents) have ill-defined commutators. However, we identify an infinite-dimensional subalgebra whose commutators are not singular, and explicitly calculate its structure constants. This constitutes a subalgebra of the gauge symmetry of string theory, although it may act on auxiliary as well as propagating fields. We term this object a {\it weighted tensor algebra}, and, while it appears to be a distant cousin of the $W$-algebras, it has not, to our knowledge, appeared in the literature before.

14 pages, Plain TeX, report RU93-8, CTP-TAMU-2/94, CERN-TH.7022/93

References in corpus (9)

• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• Connections on the State-Space over Conformal Field Theories
• Space-Time Symmetries of Quantized Tensionless Strings
• Measuring the $W$-hair of String Black Holes
• The Origin of Space-Time as $W$ Symmetry Breaking in String Theory
• Gauge Symmetries of the N=2 String
• W-Infinity Symmetry of the Nambu-Goto String in 4 Dimensions
• Deformations of CFT Beyond the First Order and Closed String Field Theory

Cited by in corpus (11)

• Stringy Symmetries and Their High-energy Limits
• Zero-norm states and High-energy Symmetries of String Theory
• Duality Symmetries and Noncommutative Geometry of String Spacetime
• T-Duality in Arbitrary String Backgrounds
• Higgs Mechanism in String Theory
• Spacetime Supersymmetry in a nontrivial NS-NS Superstring Background
• Metastring Theory and Modular Space-time
• O(d,d,Z) Transformations as Automorphisms of the Operator Algebra
• Deformations in Closed String Theory -- Canonical Formulation and Regularization
• Finite Deformations of CFT and Spacetime Geometry
• SuperHiggs Mechanism in String Theory