Quantum Hamiltonian reduction and conformal field theories

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1991

OSTI ID:7235362

Bershadsky, M

It is proved that irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of the SL (2, R) current algebra by putting a constraint on the latter using the BRST formalism. Thus there is a SL(2, R) symmetry in the Virasoro algebra which is gauged and hidden. This construction of the Virasoro algebra is the quantum analog of the Hamiltonian reduction. The author then naturally leads to consider an SL(2, R) Wess-Zumino-Witten model. This system is related to the quantum field theory of the coadjoint orbit of the Virasoro group. Based on this result he presents the canonical derivation of the SL(2, R) current algebra in Polyakov's theory of two dimensional gravity; it is manifestation of the SL(2, R) symmetry in the conformal field theory hidden by the quantum Hamiltonian reduction. He discusses the quantum Hamiltonian reduction of the SL(n, R) current algebra for the general type of constraints labeled by index 1 {le} l {le} (n {minus} 1) and claim that it leads to the new extended conformal algebras W{sub n}{sup l}. For l = 1 he recovers the well known W{sub n} algebra introduced by A. Zamolodchikov. For SL(3, R) Wess-Zumino-Witten model there are two different possibilities of constraining it. The first possibility gives the W{sub 3} algebra, while the second leads to the new chiral algebra W{sub 3}{sup 2} generated by the stress-energy tensor, two bosonic supercurrents with spins 3/2 and the U(1) current. He conjectures a Kac formula that describes the highly reducible representation for this algebra. He also makes some speculations concerning the structure of W gravity.

• Research Organization: Princeton Univ., NJ (United States)
• OSTI ID: 7235362
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CURRENT ALGEBRA
FIELD THEORIES
GRAVITATION
HAMILTONIANS
IRREDUCIBLE REPRESENTATIONS
LIMITING VALUES
MATHEMATICAL OPERATORS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SYMMETRY