Spacetime Virasoro algebra from strings on zero radiusAdS3

2003/10/17 by Paul de Medeiros, S. Prem Kumar
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Cellular algebra #Computer science #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Pure mathematics #Quantum mechanics #RADIUS #Spacetime #Theoretical physics #Virasoro algebra #Zero (linguistics) #hep-th

paper · pdf · doi:10.1088/1126-6708/2003/12/043

published as JHEP 0312:043,2003 · 23 pages, uses JHEP.cls. References added

arxiv created 2003/10/17 · openalex publication_date 2003/12/18 · arxiv updated 2011/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study bosonic string theory in the light-cone gauge on AdS₃ spacetime with zero radius of curvature (in string units) R/√(α^′)=0. We find that the worldsheet theory admits an infinite number of conserved quantities which are naturally interpreted as spacetime charges and which form a representation of (two commuting copies of) a Virasoro algebra. Near the boundary of AdS₃ these charges are found to be isomorphic to the infinite set of asymptotic Killing vectors of AdS₃ found originally by Brown and Henneaux. In addition to the spacetime Virasoro algebra, there is a worldsheet Virasoro algebra that generates diffeomorphisms of the spatial coordinate of the string worldsheet. We find that if the worldsheet Virasoro algebra has a central extension then the spacetime Virasoro algebra acquires a central extension via a mechanism similar to that encountered in the context of the SL(2,R) WZW model.Our observations are consistent with a recently proposed duality between bosonic strings on zero radius AdS_d+1 and free field theory in d dimensions.

Citations

• String Theory and the Size of Hadrons
• Lightcone Quantization of String Theory Duals of Free Field Theories
• Classical and Quantized Tensionless Strings
• String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I
• Tensionless strings, WZW models at critical level and massless higher spin fields
• On the covariant quantization of tensionless bosonic strings in AdS spacetime
• Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
• The large N limit of superconformal field theories and supergravity