Pseudo algebras and pseudo double categories.
-deformation of the Virasoro algebra and lattice conformal theories
Quantum probability, renormalization and infinite-dimensional *-Lie algebras.
Représentations des groupes quantiques
Rogers-Ramanujan identities: A century of progress from mathematics to physics.
SLE and triangles.
Some abstract properties of semigroups appearing in superconformal theories.
Space of local fields in integrable field theory and deformed abelian differentials.
Symmetries of the Kac-Peterson modular matrices of affine algebras.
TFT Construction of RCFT correlators. V: Proof of modular invariance and factorisation.
The classification of modular invariants revisited
The form factor program: a review and new results - the nested off-shell Bethe ansatz.
The geometry of Brownian surfaces.
The mathematics of fivebranes.
The Picard group of the moduli of higher spin curves.
Topics in statistical physics involving braids
We review the appearance of the braid group in statistical physics. In particular, we explain its relevance to the anyon model of fractional statistics and conformal field theory.
Tree algebras: An algebraic axiomatization of intertwining vertex operators
We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over . We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over .
-deformed WZW model and its gauging.
Universality for conformally invariant intersection exponents
We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our paper [27], we show that any set defined under such a conformal invariant measure behaves exactly as a pack (containing maybe a non-integer number) of Brownian...
Vacuum Structure of 2+1-Dimensional Gauge Theories
We analyse some non-perturbative properties of the Yang-Mills vacuum in two-dimensional spaces in the presence of Chern-Simons interactions. We show that the vacuum functional vanishes for some gauge field configurations. We have identified some of those nodal configurations which are characterized by the property of carrying a non-trivial magnetic charge. In abelian gauge theories this fact explains why magnetic monopoles are suppressed by Chern-Simons interactions. In non-abelian theories it suggests...