Related papers: Parafermionic theory with the symmetry Z_5
We prove conjectures of Zamolodchikov and Belavin-Belavin in Liouville conformal field theory (CFT), which are generalisations of the celebrated Belavin-Polyakov-Zamolodchikov equations known as the higher equations of motion.…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…
Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that $T^2=-1$ for fermionic systems. In PT-symmetric quantum mechanics an operator has both PT and CPT adjoints.…
We define a 3-algebra with structure constants being symmetric in the first two indices. We also introduce an invariant anti-symmetric tensor into this 3-algebra and call it a symplectic 3-algebra. The general N=5 superconformal…
We investigate a class of conformal Non-Abelian-Toda models representing a noncompact $SL(2,R)/U(1)$ parafermionions (PF) interacting with a specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the…
We classify all two-dimensional, unitary, rational conformal field theories with two primaries, central charge $c<25$, and arbitrary Wronskian index. In mathematical parlance, we classify all strongly regular vertex operator algebras (VOAs)…
We use fermionic operators to construct toroidal Lie algebras of classical types, including in particular that of symplectic affine algebras, which is first realized by fermions.
We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of…
The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and the fusion rules are determined.
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA),…
We study mesonic line operators in Chern-Simons theories with bosonic or fermionic matter in the fundamental representation. In this paper, we elaborate on the classification and properties of these operators using all loop resummation of…
We revisit the construction of conformal field theories based on Takiff algebras and superalgebras that was introduced by Babichenko and Ridout. Takiff superalgebras can be thought of as truncated current superalgebras with Z-grading which…
The representation theory of deformed oscillator algebras, defined in terms of an arbitrary function of the number operator~$N$, is developed in terms of the eigenvalues of a Casimir operator~$C$. It is shown that according to the nature of…
The form of realistic space-time supersymmetry is fixed, by Haag-Lopuszanski-Sohnius theorem, either to the familiar form of Poincare supersymmetry or, in massless case, to that of conformal supersymmetry. We question necessity for such…
In the context of higher gauge theory, we construct a flat and fake flat 2-connection, in the configuration space of $n$ particles in the complex plane, categorifying the Knizhnik-Zamolodchikov connection. To this end, we define the…
We show that the quantum field theoretical formulation of the $\tau$-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge…
We find a family of solutions to Zamolodchikov's tetrahedral algebra corresponding to the fermionic R-operator for the free fermion model of the difference type in one of the spectral parameters, construct an extension of the R-operator for…
We compute correlators of two heavy and two light operators in the strong coupling and large $c$ limit of the D1D5 CFT which is dual to weakly coupled AdS$_3$ gravity. The light operators have dimension two and are scalar descendants of the…