The Algebra of Diffeomorphisms from the World Sheet

Abstract

The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras.

arXiv comment16 pages

References in corpus (20)

• Target Space Duality in String Theory
• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• On BMS Invariance of Gravitational Scattering
• Aspects of the BMS/CFT correspondence
• Superspace Duality in Low-Energy Superstrings
• The gauge algebra of double field theory and Courant brackets
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Doubled α'-Geometry
• New Perspectives on the BRST-algebraic Structure of String Theory
• Connections on the State-Space over Conformal Field Theories
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Double Field Theory, T-Duality, and Courant Brackets
• On First Order Formalism in String Theory
• Nearby CFT's in the operator formalism: The role of a connection
• Gauge and General Coordinate Invariance in Non-Polynomial Closed String Field Theory
• The AdS3 central charge in string theory
• Beta-gamma systems and the deformations of the BRST operator
• Asymptotic symmetry groups and operator algebras
• Deformations in Closed String Theory -- Canonical Formulation and Regularization

Cited by in corpus (5)

• Soft Hair on Black Holes
• BMS, String Theory, and Soft Theorems
• Metastring Theory and Modular Space-time
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
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