Related papers: $N=4$ superconformal algebras and diagonal cosets
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$.…
Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension.…
The chiral algebra of a 4D $N\geq2$ superconformal field theory is a vertex operator algebra generated by the Schur subsector of the 4D theory and its rigid (yet rich) structure has been useful in constraining and classifying 4D N=2 SCFTs.…
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of…
We consider a system of D5/D1 branes in the supergravity background AdS_3xS^3xX, where X is T^4 or K3. By investigating the structure of the missing states in the conformal description, we are able to extend the AdS/CFT correspondence to W…
Possible ways of constructing extended fermionic strings with $N=4$ world-sheet supersymmetry are reviewed. String theory constraints form, in general, a non-linear quasi(super)conformal algebra, and can have conformal dimensions $\geq 1$.…
A new N=4 superconformal algebra (SCA) is presented. Its internal affine Lie algebra is based on the seven-dimensional Lie algebra su(2)\oplus g, where g should be identified with a four-dimensional non-reductive Lie algebra. Thus, it is…
Proceeding from a nonlinear realization of the most general N=4, d=1 superconformal symmetry, associated with the supergroup D(2,1;alpha), we construct a new model of nonrelativistic N=4 superconformal mechanics. In the bosonic sector it…
In this paper, it is shown that the diagonal coset vertex operator algebra $C(L_{\mathfrak{g}}(k+2,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(2,0))$ is rational and $C_2$-cofinite in case $\mathfrak{g}=so(2n), n\geq 3$ and $k$ is an…
The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal…
By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special K\"ahler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in…
In superdimension $(2|2)$ there are only three non-Abelian Lie superalgebras admitting non-degenerate ad-invariant supersymmetric metric, the well-known Lie superalgebra $gl(1|1)$, and two more, $({\C}^3 + \A)$ and $({\C}_0^5 +{\A})$. After…
A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…
Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral…
We clarify some properties of projective superspace by using a manifestly superconformal notation. In particular, we analyze the N=2 scalar multiplet in detail, including its action, and the propagator and its super-Schwinger parameters.…
Algebraic structures of N = (4; 4) and N = (8; 8) supersymmetric (SUSY) two dimensional sigma models on Lie groups (in general) and SUSY Wess-Zumino-Witten (WZW) models (as special) are obtained. For SUSY WZW models, these algebraic…
$W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebras are deformations of ${\mathfrak{bms}_3}$ and ${\mathfrak{bms}_4}$ algebra respectively. We present an $\mathcal{N}=2$ supersymmetric extension of $W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebra…
The general structure of the scalar cosets of the Maxwell-Einstein supergravities is given. Following an introduction of the non-linear coset formalism of the supergravity theories a comparison of the coset algebras of the Maxwell-Einstein…
We study realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary…
Topological conformal field theories based on superconformal current algebras are constructed. The models thus obtained are the supersymmetric version of the $G/G$ coset theories. Their topological conformal algebra is generated by…