Triangle Seminars

Abstract:
Considering an arbitrary algebraic curve E(x,y)=0, I will build a infinite families of invariants, Fg(E) and Wkg(E), wrt deformations of the complexe and modular structure of the curve. I will show that, when the curve is the spectral curve of a matrix model, i.e. the limit of the loop equations of the model when the size N of the matrix
tends to infinity, these objects give the terms of the topological ('t Hooft) expansion of the free energy and the correlations functions of the corresponding matrix model. As an exemple, if E is the spectral curve of the hermitian 2-Matrix Model, one computes the generating functions of 2-colored discretized surfaces closed or open, with boundary operators or not.

Abstract:
The integral over a group of the Harish-Chandra measure has been known for a long time. On the other side, the moments of this measure (or correlation functions) are not known in general and a general formalism to compute them is lacking. I will present a formalism that allows us to compute correlation functions of the Harish-Chandra measure for any of the classical simple groups in terms of integrals over nihilpotent algebras (triangular matrices). This formulas are, in a sense, a generalization of the Duistermaat-Heckman theorem, in other words, a localization formula.

Abstract:
We discuss a bijection between the Z_k parafermions CFT quasi-particle
basis and the RSOS lattice paths. This bijection also implies a
bijection between Bressoud lattice paths and RSOS lattice paths. We generalize this result for the graded parafermionic models and use it to construct a new fermionic character formula for the M(k+1,2k+3) minimal models, which are dual to the graded parafermions.

Abstract:
We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS5 x S5. We find the canonical su(2,2)2 invariant S-matrix satisfying the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave expansion matches exactly the leading order term recently obtained by the direct perturbative computation. We also show that the S-matrix obtained by Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter equation, and, as a consequence, the corresponding ZF algebra is twisted. The S-matrices in gauge and string theories however are physically equivalent and related by a non-local transformation of the basis states which is explicitly constructed.