Search results for "Witt algebra"

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3D SINGLETONS AND THEIR BOUNDARY 2D CONFORMAL FIELD THEORY

1999

This paper is a continuation of recent work of Flato and Frønsdal on singletons in 1+2 anti De Sitter universe and their link with 2D conformal field theories on the boundary. More specifically we show that in this framework we can construct a 3D-singleton model in the bulk, the limit of which on the boundary of De Sitter space is a Gupta–Bleuler triplet for two commuting copies of the Witt algebra. We also generalize this result to the case of WZNW models.

Primary fieldde Sitter–Schwarzschild metricDe Sitter spaceConformal field theoryWess–Zumino–Witten modelStatistical and Nonlinear PhysicsWitt algebraAnti-de Sitter spaceMathematical Physicsde Sitter invariant special relativityMathematical physicsMathematicsReviews in Mathematical Physics
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The Virasoro Algebra

1989

In this chapter we shall study the Lie algebra Vect S1 of vector fields on a circle and some of its generalizations. The Lie algebra Vect S1 has a central extension, the Virasoro algebra. The representation theory of the Virasoro algebra is closely related to the representation theory of affine Lie algebras. In fact, through the Sugawara construction, to be defined below, a highest weight representation of an affine Lie algebra carries always a highest weight representation of the Virasoro algebra. All the irreducible highest weight representations of the Virasoro algebra are known and they can be exponentiated to representations of associated infinite-dimensional Lie groups. The representa…

Filtered algebraHigh Energy Physics::TheoryPure mathematicsMathematics::Quantum AlgebraCurrent algebraCellular algebraVirasoro algebraUniversal enveloping algebraWitt algebraAffine Lie algebraMathematicsSupersymmetry algebra
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