O(N)-extended superconformal field theory in superspace

Abstract

We discuss the superspace formalism for the description of O(N)-extended superconformal quantum field theory in two dimensions. Such theories exist for N ~< 4. In O(4)-extended superconformal transformations two independent anomalous terms can be present. Under the assumption that in physical models a specific combination of these anomalies is absent, we show that the allowed values of the N = 4 Virasoro central charge c are c(n+, n_) = 6n+n_/(n++ n_).

AdS3/CFT2 correspondence and space-time N = 3 superconformal algebra

“…These currents L n , T a m , Q a r close commutation relations together with a spin 1/2 fermionic current Ψ r Ψ r = A dz 2πi e −ϕ/2 P r , These constitute a space-time N = 3 SCA [18,19,20] with central chargec = 3 2k so , (…”

String theory on AdS3×S3×S3×S1

“…Combining the global N = 4 algebra (2.35) with the full Virasoro algebra (2.12) and affine SU (2) × SU (2) × U (1), (2.15), (2.16), (2.21) (in the worldsheet BRST cohomology and using the freedom of picture changing [7]) leads to the so called "large" N = 4 superconformal algebra [8,9]. This chiral algebra is generated by a spin-2 stress tensor (whose modes are L n , n ∈ Z), four spin-3/2 fields (with modes G ij r , r ∈ Z + 1/2), seven spin-1 currents (with modes T a n , R a n , α n ), and four spin-1/2 fermions (with modes Γ ij r ).…”

Induced and effective gravity theories in D = 2

“…(2.1) is only a special case of a one parameter family of N=4 algebras. This one-parameter family of N = 4 superconformal algebras occurs both in a linearized version, discovered in [19], generalizing the Ademollo et al [43] N = 4 algebra and a non-linearly generated version, generalizing the Knizhnik-Bershadsky SO(4) [16,17] algebra, discovered in [20].…”

“…It can be obtained by folding or twisting [19] the previously mentioned linear N = 4 algebras. The resulting superconformal algebra has besides the energy-momentum tensor, 4 dimension 3/2 supercurrents and an so(3) affine Lie algebra.…”

“…These are based on a one parameter family of linear N = 4 superconformal algebras [19]. By decoupling a U(1) current and 4 fermions [20], one obtains a one parameter family of non-linearly generated N = 4 superconformal algebras.…”