Related papers: Character Expansions, Itzykson-Zuber Integrals, an…
It was conjectured by Jackson et.al. that the finite volume effective partition function of QCD with the topological charge $M-N$ coincides with the Itzyskon-Zuber type integral for $M\times N$ rectangular matrices. In the present article…
Character expansions are among the most important approaches to modern quantum field theory, which substitute integrals by combinations of peculiar special functions from the Schur-Macdonald family. These formulas allow various…
Formulas for the expansion of arbitrary invariant group functions in terms of the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a combinatorial method. The method is similar to one used by Balantekin to expand…
We find the finite volume QCD partition function for arbitrary quark masses. This is a generalization of a result obtained by Leutwyler and Smilga for equal quark masses. Our result is derived in the sector of zero topological charge using…
In theories with supersymmetry, we can calculate a special partition function, known as the superconformal index. In particular, for a gauge group of $\mathrm{U}(N)$ and particles belonging to the adjoint representation, there is a fast…
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of…
The partition functions of QCD2 on simple surfaces admit representations in terms of exponentials of the inverse coupling, that are modular transforms of the usual character expansions. We review the construction of such a representation in…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally…
The color-flavor transformation for the unitary group (Zirnbauer 1996) is extended to the special unitary group. The resulting partition function is represented as sum over disconnected sectors characterized by a U(1)-charge. Application to…
In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…
We compute the Itzykson-Zuber (IZ) integral for the superunitary group U(m|n). As a consequence, we are able to find the non-zero correlations of superunitary matrices
We consider character expansion of tau functions and multiple integrals in characters of orhtogonal and symplectic groups. In particular we consider character expansions of integrals over orthogonal and over symplectic matrices.
We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus in the gauge $\partial_{0} A_{0} = 0$ by integrating explicitly over the non zero modes of the Fourier expansion in the periodic time variable. The…
We compute an analogue of the Itzykson-Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson-Zuber diffusion equation method to the space of…
I explore the possibility of finding an equivalent string representation of two dimensional QCD. I develop the large N expansion of the ${\rm QCD_2}$ partition function on an arbitrary two dimensional Euclidean manifold. If this is related…
We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical…
We present a tensor-network formulation for the strong-coupling expansion of QCD with staggered quarks at nonzero chemical potential, for arbitrary number of dimensions, colors, and flavors. We integrate out the gauge and quark degrees of…
We demonstrate the consistency of character expansion for the Itzykson-Zuber (IZ) model in terms of Schur polynomials with the old formulas for pair correlators with the IZ measure. An essential new feature of the correlators is that they…
A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations…