Results of the classification of superconformal algebras in two dimensions

Abstract

A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously known cases and the constructed in our previous paper exceptional $N=8$ superalgebra associated with $F(4)$, a novel exceptional $N=7$ superconformal algebra associated with $G(3)$ is found, as well as a whole family of superalgebras containing affine ${\widehat{su}}_2\oplus {\widehat{usp}}_{2N}$. A classification scheme for quasisuperconformal algebras is also outlined.

9 pages

Cited by in corpus (36)

• W-symmetry in Conformal Field Theory
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity
• AdS${}_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry
• AdS${}_3$ solutions with exceptional supersymmetry
• Fundamental Strings, Holography, and Nonlinear Superconformal Algebras
• Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras
• A Unified Approach to the Minimal Unitary Realizations of Noncompact Groups and Supergroups
• On the coset duals of extended higher spin theories
• All $\mathcal{N}=(8,0)$ AdS${}_3$ solutions in 10 and 11 dimensions
• Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• Real forms of nonlinear superconformal and quasi-superconformal algebras and their unified realization
• Maximally $\mathcal{N}$-extended super-BMS${}_3$ algebras and Generalized 3D Gravity Solutions
• Free Field Representations of Extended Superconformal Algebras
• Supergroup - extended super Liouville correspondence
• Unitary representations of SW(3/2,2) superconformal algebra
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• AdS${}_3\times$ S${}^2$ in IIB with small $\mathcal{N}=(4,0)$ supersymmetry
• Vacua and RG flows in N=9 three dimensional gauged supergravity
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• Supersymmetric Field Theories on AdS_p x S^q
• How Many $N=4$ Strings Exist ?
• Constructing Classical and Quantum Superconformal Algebras on the Boundary of AdS_3
• BRST Operator for Superconformal Algebras with Quadratic Nonlinearity
• Vacua of N=10 three dimensional gauged supergravity
• 3D N=6 Gauged Supergravity: Admissible Gauge Groups, Vacua and RG Flows
• Recent advances and open questions on the susy structure of the chiral de Rham Complex
• Ramond sector of superconformal algebras via quantum reduction
• Gaugings of N=4 three dimensional gauged supergravity with exceptional coset manifolds
• Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited
• Physical states for non-linear $SO(N)$ strings
• New constrained generalized Killing spinor field classes in warped flux compactifications
• Seven Sphere and the Exceptional Nonlinear Superconformal Algebras