We study realizations of the exceptional non-linear (quadratically generated, or W type) N = 8 and N = 7 superconformal algebras with Spin(7) and G2 affine symmetry currents, respectively. Both the N = 8 and N = 7 algebras admit unitary highestweight representations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G2, with the central charges c8 = 26/5 and c7 = 5, respectiv...

Let G be an affine group scheme of finite type over a global field F . (We do not assume G to be reductive or smooth or connected.) Let AF denote the locally compact adele ring of F , S be a finite non-empty set of places of F that contains the archimedean places, and AF the factor ring of adeles with vanishing component along S; for FS = ∏ v∈S Fv, we have AF = FS ×AF . Recall that if X is a fi...

We consider the Feigin-Fuchs-Felder formalism of the SU(2)k×SU(2)l/SU(2)k+l coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges, one associated with the parafermion sector and the other associated with the minimal sector in the theory. The usual screened vertex operator is extended to the BRST invar...

In these lectures we report recent work on the exact quantization of dimensionally reduced gravity [1, 2, 3, 4]. Assuming the presence of commuting Killing symmetries which effectively eliminate the dependence on all but two space-time coordinates allows us to cast the models into the form of 2d non-linear (G/H)-coset space σ-models coupled to gravity and a dilaton. This construction includes a...

In this letter we consider higher-dimensional Yang–Mills theories and examine their consistent coset space dimensional reduction. Utilizing a suitable ansatz and imposing a simple set of constraints we determine the four-dimensional gauge theory obtained from the reduction of both the higher-dimensional Lagrangian and the corresponding equations of motion. The two reductions yield equivalent re...

Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating nitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such presentation. We show that it is much easier than it rst appears, albeit at the ...

The construction of flat currents, and hence conserved non-local charges, for the superstring on AdS5 × S 5 is generalised. It is shown that such currents exist for sigma-model type actions on all coset (super-)spaces G/H in which, at the level of the Lie algebras, h is the grade-zero subspace of a Zm-grading of g. This is true for an essentially unique choice of the Wess-Zumino term, which is ...

Geometric quantization on a coset space G/H is considered, intending to recover Mackey’s inequivalent quantizations. It is found that the inequivalent quantizations can be obtained by adopting the symplectic 2-form which leads to Wong’s equation. The irreducible representations of H which label the inequivalent quantizations arise from Weil’s theorem, which ensures a Hermitian bundle over G/H t...

We propose a rational quantum deformed nonlocal currents in the homogenous space SU(2)k/U(1), and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k = c is obtained. In the classical limit h̄ → 0, the quantum nonlocal currents become SU(2)k parafermion, and the realization of Yangian double becomes the parafermion realization o...