16125045
Vertex Operator Algebra Arising from the Minimal Series M (3, p ) and Monomial Basis
We study a vertex operator algebra (VOA)Vrelated to the M(3, p) Virasoro minimal series. This VOA reduces in the simplest case p = 4 to the level-two integrable vacuum module of \({\widehat {sl}_2}\). On V there is an action of a commutative current a(z), which is an analog of the current e(z) of \({\widehat {sl}_2}\). Our main concern is the subspace W generated by this action from the highest weight vector of V. Using the Fourier components of a(z), we present a monomial basis of W and a semi-infinite monomial basis of V. We also give a Gordon type formula for their characters.
34870247
Vertex operators in solvable lattice models
The basic properties of q‐vertex operators are formulated in the context of the Andrews–Baxter–Forrester (ABF) series, as an example of face interaction models, the q‐difference equations satisfied by their correlation functions are derived, and their connection with representation theory established. The q‐difference equations of the Kashiwara–Miwa (KM) series are discussed as an example of edge interaction models. Next, the Ising model, the simplest special case of both ABF and KM series, is studied in more detail using the Jordan–Wigner fermions. In particular, all matrix elements of vertex operators are calculated.
119324041
Asymptotic representations and Drinfeld rational fractions
We introduce and study a category of representations of the Borel algebra, associated with a quantum loop algebra of non-twisted type. We construct fundamental representations for this category as a limit of the Kirillov-Reshetikhin modules over the quantum loop algebra and we establish explicit formulas for their characters. We prove that general simple modules in this category are classified by n-tuples of rational functions in one variable, which are regular and non-zero at the origin but may have a zero or a pole at infinity.
11481265
Reduced qKZ Equation and Correlation Functions of the XXZ Model
Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (λ1, . . . ,λ2n) as (λ1, . . . ,λn,λn+1, . . . ,λ1+1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functions ,ω with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice of ,ω. We also present a conjectural formula in the massless regime.
131772242
Holonomic Quantum Fields
The present chapter V of our series is an application of the theory of rotation ([!]) to the lattice models. Included here are the two-dimensional Ising model ([5], [6]), a bosonic counterpart of it, the one-dimensional XY model ([12]) and the free fermion model ([14] [15] [16]). In each case we shall compute exactly the norm representation of spin operators, and hence their n-point correlation functions. The materials in this article are "time-ordered" according to the development, but we could have unified the treatment by using the path integral formalism exposed in Section 5.4 (symplectic case) and in Section 5.7 (orthogonal case). Since the first announcement of our result on the Ising model ([2] [4]), there have appeared several independent papers [9] [10] [11] that deal with the exact computation of n-point functions. We emphasize that these results are made most transparent by considering directly the explicit form of spin operators. (For instance the arbitrariness in the infinite series expression of n-point functions for T>TC is neatly described in this way. See p. 548.) The plan of this paper is as follows. The first three sections 5.1-5.3 are devoted to the Ising model. We shall see that a systematic application of the original method of Onsager ([5]) enables one to express explicitly not only the free energy but also the spin operator itself. We first review the diagonalization procedure of the Hamiltonian (see [5] [7]) in Section 5.1, and compute the norm representation of spin operators in Section 5.2. Using these results we derive in Section 5.3 infinite series expressions for n-point correlation functions (an application of the product formula in [1]). We also verify their convergence and several symmetry properties. In Section 5.4 we present a two-
14644136
Smirnov's integrals and the quantum Knizhnik-Zamolodchikov equation of level 0
We study the quantum Knizhnik-Zamolodchikov equation (1984) of level 0 associated with the spin 1/2 representation of Uq(SL2). We find an integral formula for solutions in the case of an arbitrary total spin and mod q mod <1. In the formula, different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed.
56104929
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.
117876117
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.
119094900
A System for the Automatic Computation of Cross-Sections Including SUSY Particles
We introduce a new method to treat Majorana fermions on the GRACE system, which has already been developed for the computation of the matrix elements for the processes of the standard model. In the standard model, we already have included such particles as Dirac fermions, gauge bosons and scalar bosons in the system. On the other hand, there are four Majorana fermions called neutralinos in the minimal SUSY standard model (MSSM). In consequence, we have constructed a system for the automatic computation of cross-sections for the processes of the MSSM. It is remarkable that our system is also applicable for another model including Majorana fermions once the definition of the model file is given.
125557202
Analytical Approach to Single Selectron Production
15619161
Automatic Calculation of SUSY-particle Production )
AbstractWe introduce a new method to treat Majorana fermions and interactions with fermion-number violation on the GRACE system which has been developed for the automatic com-putation of the matrix elements for the processes of the standard model. Thus we haveconstructed a system for the automatic computation of cross-sections for the processes of theminimal SUSY standard model (MSSM). 1 Introduction At the theoretical point of view, it has been a promising hypothesis that there exists a symmetry calledsupersymmetry (SUSY) between bosons and fermions at the uniﬁcation-energy scale. It, however, is abroken symmetry at the electroweak-energy scale. Thus the relic of SUSY is expected to remain as a richspectrum of SUSY particles, partners of usual matter fermions, gauge bosons and Higgs scalars, namedsfermions, gauginos and higgsinos, respectively [1].The quest of these new particles has already been one of the most important pursuits to the presenthigh-energyphysics[2]. Although suchparticleshavenot yet been discovered, massesofthem areexpectedto be O(10