Searcharxiv⌕ Search

arXiv subjects

M. Jimbo

Publications and source records attributed to M. Jimbo.

At least 37 records · Page 2Linked to original sources
arXiv2014

Creation operators for the Fateev-Zamolodchikov spin chain

In our previous works on the XXZ chain of spin one half, we have studied the problem of constructing a basis of local operators whose members have simple vacuum expectation values. For this purpose a pair of fermionic creation operators have been introduced. In this article we extend this construction to the spin one case. We formulate the fusion procedure for the creation operators, and find a triplet of bosonic as well as two pairs of fermionic creation operators. We show that the resulting basis of local operators satisfies the dual reduced qKZ equation.

hep-th↗
arXiv2013

Hidden Grassmann structure in the XXZ model V: sine-Gordon model

We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on the plane. In the present paper we make an essential addition by giving a connection between various primary fields in terms of yet another kind of fermions. The one-point functions of primary fields and descendants are expressed in terms of a single function defined via the data from the thermodynamic Bethe Ansatz equations.

hep-th↗
arXiv2012

Representations of quantum toroidal $gl_n$

We define and study representations of quantum toroidal $gl_n$ with natural bases labeled by plane partitions with various conditions. As an application, we give an explicit description of a family of highest weight representations of quantum affine $gl_n$ with generic level.

math.QA↗
arXiv2012

Pair-production and Three-body Decay of the Lighter Stop at the ILC in One-loop Order in the MSSM

We have been developing a program package called GRACE/SUSY-loop which automatically calculates the MSSM amplitudes in one-loop order. We present numerical results of calculations for pair-production and three-body decay of the lighter stop ($\widetilde{t}_1$) at the International Linear Collider (ILC) using GRACE/SUSY-loop. Since the distributions of missing transverse energy (MET) depend on mass spectrum of SUSY particles, we consider two scenarios on three-body decay of $\widetilde{t}_1$. In these scenarios, both QCD and EW corrections have positive sign for decay widths and cross sections.

hep-ph↗
arXiv2011

Quantum toroidal $\mathfrak{gl}_1$ algebra : plane partitions

In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the corresponding formal characters. As an application we obtain a Gelfand-Zetlin type basis for a class of irreducible lowest weight $\gl_\infty$-modules.

math.QA↗
arXiv2010

Present Status of GRACE/SUSY-loop

GRACE/SUSY-loop is a program package for the automatic calculation of the MSSM amplitudes in one-loop order. We present features of GRACE/SUSY-loop, processes calculated using GRACE/SUSY-loop and an extension of the non-linear gauge formalism applied to GRACE/SUSY-loop.

hep-ph↗
arXiv2010

Hidden Grassmann Structure in the XXZ Model IV: CFT limit

The Grassmann structure of the critical XXZ spin chain is studied in the limit to conformal field theory. A new description of Virasoro Verma modules is proposed in terms of Zamolodchikov's integrals of motion and two families of fermionic creation operators. The exact relation to the usual Virasoro description is found up to level 6.

hep-th↗
arXiv2010

Quantum continuous $\mathfrak{gl}_\infty$: Semi-infinite construction of representations

We begin a study of the representation theory of quantum continuous $\mathfrak{gl}_\infty$, which we denote by $\mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of difference operators acting on the space of Laurent polynomials in one variable. Fundamental representations of $\mathcal E$ are labeled by a continuous parameter $u\in {\mathbb C}$. The representation theory of $\mathcal E$ has many properties familiar from the representation theory of $\mathfrak{gl}_\infty$: vector representations, Fock modules, semi-infinite constructions of modules. Using tensor products of vector representations, we construct surjective homomorphisms from $\mathcal E$ to spherical double affine Hecke algebras $S\ddot H_N$ for all $N$. A key step in this construction is an identification of a natural bases of the tensor products of vector representations with Macdonald polynomials. We also show that one of the Fock representations is isomorphic to the module constructed earlier by means of the $K$-theory of Hilbert schemes.

math.QA↗
arXiv2010

Quantum continuous $gl_\infty$: Tensor products of Fock modules and $W_n$ characters

We construct a family of irreducible representations of the quantum continuous $gl_\infty$ whose characters coincide with the characters of representations in the minimal models of the $W_n$ algebras of $gl_n$ type. In particular, we obtain a simple combinatorial model for all representations of the $W_n$-algebras appearing in the minimal models in terms of $n$ interrelating partitions.

math.QA↗
arXiv2010

Systematic study of 1-loop correction on sparticle decay widths using GRACE/SUSY-loop

The 1-loop corrected decay widths of sparticles (charginos, neutralinos, gluino and sfermions) in the framework of the MSSM are calculated systematically using GRACE/SUSY-loop, which is the program package for the automatic calculation of the MSSM amplitudes in the 1-loop order. We present the renormalization scheme used in our system and show some numerical results of decay widths of sfermions and gluino using the SPS1a' parameter set and other SUSY parameter sets.

hep-ph↗
arXiv2009

Gelfand-Zetlin basis, Whittaker vectors and a bosonic formula for the $\sln$ principal subspace

We derive a bosonic formula for the character of the principal space in the level $k$ vacuum module for $\widehat{\mathfrak{sl}}_{n+1}$, starting from a known fermionic formula for it. In our previous work, the latter was written as a sum consisting of Shapovalov scalar products of the Whittaker vectors for $U_{v^{\pm1}}(\mathfrak{gl}_{n+1})$. In this paper we compute these scalar products in the bosonic form, using the decomposition of the Whittaker vectors in the Gelfand-Zetlin basis. We show further that the bosonic formula obtained in this way is the quasi-classical decomposition of the fermionic formula.

math.QA↗
arXiv2008

Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction

We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio $ρ(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $ω(\z,ξ)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.

math-ph↗
arXiv2008

Hidden Grassmann Structure in the XXZ Model II: Creation Operators

In this article we unveil a new structure in the space of operators of the XXZ chain. We consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the disorder operator itself is considered as primary field. In our previous paper, we have introduced the annhilation operators which mutually anti-commute and kill the primary field. Here we construct the creation counterpart and prove the canonical anti-commutation relations with the annihilation operators. We show that the ground state averages of quasi-local operators created by the creation operators from the primary field are given by determinants.

hep-th↗
arXiv2007

Principal $\hat{sl}(3)$ subspaces and quantum Toda Hamiltonian

We study a class of representations of the Lie algebra of Laurent polynomials with values in the nilpotent subalgebra of sl(3). We derive Weyl-type (bosonic) character formulas for these representations. We establish a connection between the bosonic formulas and the Whittaker vector in the Verma module for the quantum group $U_v sl(3)$. We also obtain a fermionic formula for an eigenfunction of the sl(3) quantum Toda Hamiltonian.

math.QA↗
arXiv2007

Fermionic basis for space of operators in the XXZ model

In the recent study of correlation functions for the infinite XXZ spin chain, a new pair of anti-commuting operators $b(z), c(z)$ was introduced. They act on the space of quasi-local operators, which are local operators multiplied by the disorder operator. For the inhomogeneous chain with the spectral parameters $ξ_{k}$, these operators have simple poles at $z^2=ξ_{k}^2$. The residues are denoted by $b_{k}, c_{k}$. At $q=i$, we show that the operators $b_{k}, c_{k}$ are cubic monomials in free fermions. In other words, the action of these operators is very simple in the fermion basis. We give an explicit construction of these fermions. Then, we show that the existence of the fermionic basis is a consequence of the Grassmann relation, the equivariance with respect to the action of the symmetric group and the reduction property, which are all valid for the operators $b_{k}, c_{k}$ in the case of generic $q$.

hep-th↗