Constructing Classical and Quantum Superconformal Algebras on the Boundary of AdS_3

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.Comment: 29 pages, LaTeX, extends hep-th/990518

Conformal higher-spin symmetries in twistor string theory

It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains $psl(4|4,\mathbb R)$ superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to $SL(4|4,\mathbb R)$ one.Comment: 20 pages, LaTeX. v2: section 3 undergone major revision, others - minor improvements including correction of typos. Version accepted to Nuclear Physics

Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole

We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z_2-graded Poisson, or quantum super- algebra, which may be treated as a nonlinear generalization of the $osp(2|2)\oplus su(2)$. In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2|2) spin operator. As an odd integral, the osp(2|2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra.Comment: 13 pages; comments and ref added; V.3: misprints corrected, journal versio