相关论文: Fermionic construction of partition functions for …

The spinor-vector duality was discovered in free fermionic constructions of the heterotic-string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly free extra $Z^\prime$ symmetry that may…

We consider series over Young diagrams of products of Schur functions $s_{\lambda\cup\lambda}$, marked with ``fat partitions'' $\lambda\cup\lambda$, which appear in matrix models associated with ensembles of symplectic and orthogonal…

We propose a 2-Higgs doublet model where the symmetry is extended by $S_{3}\otimes Z_{3}\otimes Z_{3}^{\prime }\otimes Z_{14}$ and the field content is enlarged by extra $SU(2)_{L}$ singlet scalar fields. $S_3$ makes the model predictive…

We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times…

We give a detailed account of the N -component Toda lattice hierarchy. This hierarchy is an extended version of the one introduced by Ueno and Takasaki. Our version contains N discrete variables rather than one. We start from the Lax…

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…

Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z2xZ2…

We define and compute the continuous orbifold partition function and a generating function for all $n$-point correlation functions for the rank two free fermion vertex operator superalgebra on a genus two Riemann surface formed by…

We obtain the collection of symmetric and symplectic matrix integrals and the collection of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specific elements in the Spin-group orbit of the vacuum vector of…

We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a…

Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D_3. After building the vector-valued modular forms in the…

The Hermitian, complex and fermionic two-matrix models with infinite set of variables are constructed. We show that these two-matrix models can be realized by the $W$-representations. In terms of the $W$-representations, we derive the…

A recent paper of Bump, McNamara and Nakasuji introduced a factorial version of Tokuyama's identity, expressing the partition function of a six vertex model as the product of a t-deformed Vandermonde and a Schur function. Here we provide an…

We obtain large N asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i<j}(x_i-x_j)^2 \prod_{j=1}^N e^{-N V(x_j)}dx_j,\] in the case where the external potential $V$ is a polynomials such that…

We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with $N$ fermionic particles, where $N$ tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit…

The wavefunction of the free-fermion six-vertex model was found to give a natural realization of the Tokuyama combinatorial formula for the Schur polynomials by Bump-Brubaker-Friedberg. Recently, we studied the correspondence between the…

The first particle physics observable whose origin may be sought in string theory is the triple replication of the matter generations. The class of Z2XZ2 orbifolds of six dimensional compactified tori, that have been most widely studied in…

Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix…

$Q$-systems and $T$-systems are systems of integrable difference equations that have recently attracted much attention, and have wide applications in representation theory and statistical mechanics. We show that certain $\tau$-functions,…

In this paper, we present a new algebraic description of Ikeda-Naruse's $K$-theoretic Schur $P$- and $Q$-functions and their dual functions in terms of neutral fermion operators. We introduce four families of ``$\beta$-deformed…