Remarks on BMS3 invariant field theories: Correlation functions and nonunitary CFTs

2018/02/28 by Thiago Araujo, Thiago Araújo
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Chemistry #Combinatorics #Crystal structure #Crystallography #Generator (circuit theory) #Geometry #Isomorphism (crystallography) #Mathematical physics #Mathematics #Nilpotent #Nonlinear Waves and Solitons #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Symmetry (geometry) #hep-th

paper · pdf · doi:10.1103/physrevd.98.026014

published as Phys. Rev. D 98, 026014 (2018) · 21 pages; v2: presentation improved, typos corrected, references added

openalex created_date 2018/03/06 · openalex publication_date 2018/07/10 · arxiv created 2018/07/14 · arxiv updated 2018/07/17 · openalex updated_date 2026/08/05

Abstract

We use the isomorphism between the BMS₃ and the W(2,2) algebras to reconsider some generic aspects of conformal field theories (CFTs) with the BMS₃ algebra defined as a chiral symmetry. For unitarity theories, it is known that the extended symmetry generator acts trivially, and the resulting theory is equivalent to a CFT with a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending on a nilpotent variable, and we organize the Verma module through the action of this new operator. Finally, we find the conditions imposed by the modified Ward identity.

Citations

• Conformal field theory on the plane
• W-algebra W(2,2) and the vertex operator algebra L(1/2,0)⊗ L(1/2,0)
• Three-Dimensional Gravity Revisited
• Aspects of flat/CCFT correspondence
• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Infinite conformal symmetry in two-dimensional quantum field theory
• Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory
• Operator product expansion and conservation laws in non-relativistic conformal field theories
• Galilean conformal algebras in two spatial dimension
• Flat-space energy-momentum tensor from BMS/GCA correspondence
• Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Classical and quantum conformal field theory
• The Large-N Limit of Superconformal Field Theories and Supergravity
• Asymptotic Symmetries in Gravitational Theory
• The nuts and bolts of the BMS bootstrap
• BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY
• Correlation functions in conformal Toda field theory II
• Conformal Field Theory
• Introduction to Conformal Field Theory: With Applications to String Theory
• Supersymmetric Mechanics -- Vol. 3: Attractors and Black Holes in Supersymmetric Gravity