Related papers: Localization in GWZW and Verlinde formula
We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a…
We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\Tr (\Phi_1 (z_1)\ldots \Phi_n…
The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFT's associated to loop groups, as twisted equivariant K-theory. We build on their work to…
We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.
We prove a multiplicity formula for Riemann-Roch numbers of reductions of Hamiltonian actions of loop groups. This includes as a special case the factorization formula for the quantum dimension of the moduli space of flat connections over a…
The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with $SL(2,\mathbb{C})$-valued monodromy on Riemann surfaces of genus zero with $n$ punctures can be solved by taking suitable linear…
Inspired by an extension of Wiener's lemma on the relation of measures $\mu$ on the unit circle and their Fourier coefficients $\widehat{\mu}(k_n)$ along subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19,…
A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by…
Fusion rules for Wess-Zumino-Witten (WZW) models at fractional level can be defined in two ways, with distinct results. The Verlinde formula yields fusion coefficients that can be negative. These signs cancel in coset fusion rules, however.…
Following Nag-Sullivan, we study the representation of the group ${\rm Diff}^+(S^1)$ of diffeomorphisms of the circle on the Hilbert space of holomorphic functions. Conformal welding provides a triangular decompositions for the…
We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We prove a Wiener-Tauberian theorem for $L^1$-spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz theorem for complex groups. As a corollary we obtain a Wiener-Tauberian type theorem for for…
We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a weighted projective space $\mathbb{WCP}_{[n_1,n_2]}^1$, often referred to as a spindle. Starting from the spindle solution of five-dimensional minimal…
We study the gluing theory of Riemann surfaces using formal algebraic geometry, and give computable relations between the associated parameters for different gluing processes. As its application to the Liouville conformal field theory, we…
We announce the following result and give several applications: A Hamiltonian $T$-space (for $T$ a torus) with isolated fixed points is cobordant to a disjoint union of weighted projective spaces which are constructed from its fixed point…
Recently, multi-graviton theory on a simple closed circuit graph corresponding to the $S^1$ compactification of the Kaluza-Klein (KK) theory has been considered. In the present paper, we extend this theory to that on a general graph and…
We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem applied to commutative algebras. This allows considerable…
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion…
For a set of maps of based spaces $S$ we construct a version of Weiss' orthogonal calculus which depends only on the $S$-local homotopy type of the functor involved. We show that $S$-local homogeneous functors of degree $n$ are equivalent…