Hamiltonian reduction and classical extended superconformal algebras

Abstract

We present a systematic construction of classical extended superconformal algebras from the hamiltonian reduction of a class of affine Lie superalgebras, which include an even subalgebra sl(2). In particular, we obtain the doubly extended N = 4 superconformal algebraà γ from the hamiltonian reduction of the exceptional Lie superalgebra D(2|1; γ/(1 − γ)). We also find the Miura transformation for these algebras and give the free field representation. A W -algebraic generalization is discussed.

Extended superconformal algebras and free field realizations from Hamiltonian reduction

“…[6,7,8]. The new results of the present paper are that we have obtained expressions for the algebras and for the free field realizations of these algebras, which are not only completely general, but also very simple compared to previous expressions.…”

“…One method is based on the Miura transformation, used in the case of hamiltonian reduction for non-exceptional simple Lie algebras [2]. This formulation has been generalized to the extended superconformal algebras for Lie superalgebras sl(N|2) and osp(N|2) [6]. However for the remaining Lie (super)algebras, especially exceptional type algebras, it is difficult to find the explicit form of the Miura transformations.…”

“…The generic gauge transformation projected on the DS gauge slice becomes the transformation corresponding to the extended superconformal algebra, see [6,8] for details. the Poisson bracket structure on the reduced phase space can be conveniently written in terms of formal "operator product expansions".…”

Real forms of non-abelian Toda theories and their W-algebras

“…Let us now consider the implications for the W-symmetries of this model. The complex algebra W(osp(4|2) c , osp(2|2) c ) is equivalent to the complex version of the so-called 'large' N = 4 algebra, which contains an so(4) Kac-Moody symmetry [14,18]. But, since we are working in an N = 1 superspace formalism, this algebra will arise in an unusual basis consisting of the super-stress tensor T , three spin-one superfields G 0 , G ± and three spin-half superfields J 0 , J ± .…”

Classical hamiltonian reduction on D(2|1;α) Chern–Simons gauge theory and large N=4 superconformal symmetry

“…Here we formulate the D(2|1; α) CSGT and present a way to its connection with 2d large N = 4 SCFT, adopting the idea of hamiltonian reduction technique (HR method) [8,9], which is well-known in 2d CFT.…”