Related papers: Classical A_n--W-Geometry
We consider a 4d non-linear sigma model on the coset $(\mathrm{SU}(N)_L \times \mathrm{SU}(N)_R \times \mathrm{SU}(2))/(\mathrm{SU}(N)_{L+R}\times \mathrm{U}(1))\cong \mathrm{SU}(N) \times S^2$, that features a topological…
In the same way the folding of the Dynkin diagram of A_{2n} (resp. A_{2n-1}) produces the B_n (resp. C_n) Dynkin diagram, the symmetry algebra W of a Toda model based on B_n (resp. C_n) can be seen as resulting from the folding of a…
We study symmetries and dynamics of chiral $SU(N)$ gauge theories with matter Weyl fermions in a two-index symmetric ($\psi$) or anti-symmetric tensor ($\chi$) representation, together with $N \pm 4 + p $ fermions in the anti-fundamental…
The higher-spin geometries of $W_\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic…
For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space one can naturally introduce two Gauss maps and Weierstrass representation. In this paper we investigate their global geometry systematically. The…
We study the covariance properties of the equations satisfied by the generating functions of the chiral operators R and T of supersymmetric SO(N)/Sp(N) theories with symmetric/antisymmetric tensors. It turns out that T is an affine…
We investigate local and metric geometry of weighted Carnot-Carath\'eodory spaces which are a wide generalization of sub-Riemannian manifolds and arise in nonlinear control theory, subelliptic equations etc. For such spaces the intrinsic…
We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of…
The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using…
The new great development in Physics could be related to the excited progress of a new mathematics: ternary theory of numbers, ternary Pithagor theorem and ternary complex analysis, ternary algebras and symmetries, ternary Clifford…
The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by…
This is a PhD thesis in low-dimensional topology. Its main purpose is to examine so-called t\^ete-\`a-t\^ete twists. Those were defined by A'Campo and give an easy combinatorial description of certain mapping classes on surfaces with…
Generalising the chiral boundary conditions of $\mathbb{R}^{1,3}$ gravity for AdS$_4$ gravity, we derive chiral locally AdS$_4$ solutions in the Newman-Unti gauge consistent with a variational principle whose asymptotic symmetry algebra we…
It is the aim of this paper to transfer to generalised geometry tools employed in the study of semi-Riemannian immersions, specializing at times to semi-Riemannian hypersurfaces. Given an exact Courant algebroid $E \to M$ and an immersion…
Chiral QED with a generalized Fadeevian regularization is considered. Imposing a chiral constraint a gauged version of Floranini-Jackiw lagrangian is constructed. The imposition of the chiral constarint has spoiled t he manifestly Lorentz…
We discuss the $N=2$ super $W$ algebras from the hamiltonian reduction of affine Lie superalgebras $A(n|n-1)^{(1)}$ and $A(n|n)^{(1)}$. From the quantum hamiltonian reduction of $A(n|n-1)^{(1)}$ we get the free field realization of $N=2$…
It is shown how the theory of classical $W$--algebras can be formulated on a higher genus Riemann surface in the spirit of Krichever and Novikov. An intriguing relation between the theory of $A_1$ embeddings into simple Lie algebras and the…
We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional…