Related papers: Toda tau functions with quantum torus symmetries
Using the free fermions technique and non-abelian bosonization rules we introduce the multi-component Pfaff-Toda hierarchy. The tau-function is defined as vacuum expectation value of a Clifford group element of the algebra of…
In our previous work \cite{LNS}, we constructed quasi-Casoratian solutions to the noncommutative $q$-difference two-dimensional Toda lattice ($q$-2DTL) equation by Darboux transformation, which we can prove produces the existing Casoratian…
In this paper, we investigated four applications of the gauge transformation for the BKP hierarchy. Firstly, it is found that the orbit of the gauge transformation for the constrained BKP hierarchy defines a special $(2 +1)$-dimensional…
The dDS (dispersionless Davey-Stewartson) hierarchy is constructed by two eigenfunctions of a special vector field. This hierarchy consists the infinite symmetries of the dDS system. Further, this paper explores the tau function, the…
A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point…
The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU(infty) SDYM equations…
Okounkov's generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. This tau function turns into a tau function of the lattice KP…
Affine Toda equations based on simple Lie algebras arise by imposing zero curvature condition on a Lax connection which belongs to the corresponding loop Lie algebra in the principal gradation. In the particular case of $A_n^{(1)}$ Toda…
We consider the topological string partition function, including the Nekrasov deformation, for type IIB geometries with an A_{n-1} singularity over a Riemann surface. These models realize the N=2 SU(n) superconformal gauge systems recently…
We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the…
Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the…
This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the corresponding complete flag variety. The motivation comes from the…
Matrix elements in different representations are connected by quadratic relations. If matrix elements are those of a $\textit{group element}$, i.e. satisfying the property $\Delta(X) = X\otimes X$, then their generating functions obey…
We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both…
We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it…
In this paper, we firstly give the definition of dipersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov-Schulman's $\M_L$, $\M_R$ operator and give the additional Block symmetry of dBTH.…
For an arbitrary $p$, propose a new and computable method which can determine the values of unknown constants in constraints on a tau function which satisfies both the p-reduced KP hierarchy and the sting equation. All the constants do not…
A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor…
We consider $N=1$ supersymmetric Toda theories which admit a fermionic untwisted affine extension, i.e. the systems based on the $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ superalgebras. We construct the superspace Miura trasformations which allow…
We focus in this work to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the…