Constructing Classical and Quantum Superconformal Algebras on the Boundary of AdS_3

TL;DR

This paper constructs explicit classical and quantum superconformal algebras on the boundary of AdS_3 using free field realizations, revealing new asymmetric structures for N>2 that extend the understanding of AdS/CFT correspondence.

Contribution

It introduces a novel construction of superconformal algebras on AdS_3 boundaries, including explicit classical forms and evidence for quantum versions, highlighting new asymmetric properties for N>2.

Findings

Constructed explicit Virasoro and supercurrents for N even.

Discovered new asymmetric superconformal algebra structures for N>2.

Provided classical algebra for N=4 with novel features.

Abstract

Motivated by recent progress on the correspondence between string theory on anti-de Sitter space and conformal field theory, we address the question of constructing space-time N extended superconformal algebras on the boundary of AdS_3. Based on a free field realization of an affine SL(2|N/2) current superalgebra residing on the world sheet, we construct explicitly the Virasoro generators and the N supercurrents. N is even. The resulting superconformal algebra has an affine SL(N/2) \otimes U(1) current algebra as an internal subalgebra. Though we do not complete the general superalgebra, we outline the underlying construction and present supporting evidence for its validity. Particular attention is paid to its BRST invariance. In the classical limit where the free field realization may be substituted by a differential operator realization, we discuss further classes of generators needed in the closure of the algebra. We find sets of half-integer spin fields, and for N>4 these include generators of negative weights. An interesting property of the construction is that for N>2 it treats the supercurrents in an asymmetric way. Thus, we are witnessing a new class of superconformal algebras not obtainable by conventional Hamiltonian reduction. The complete classical algebra is provided in the case N=4 and is of a new and asymmetric form.