10951415
Variant of ADHMN construction associated with q-analysis
A q-deformation of the ADHMN caloron construction is considered, under which the anti-self-dual (ASD) conditions of the gauge fields are preserved. It is shown that the q-dependent Nahm data with certain constraints are crucial to determine the ASD gauge fields, as in the case of ordinary caloron construction. As an application of the q-deformed ADHMN construction, we give a q-deformed caloron of Harrington-Shepard type. Some limits of the parameters are also considered.
119295097
Numerical Nahm transform for 2-caloron solutions
Abstract A new numerical method for performing the Nahm transform for charge k = 2 caloron is presented. The Weyl equations with boundary impurities are solved directly and the determination of the appropriate basis to the linear system is established. The action densities of the 2-calorons with 10 moduli parameters are shown.
122871379
Selfdual solution of classical yang—mills fields through a q-analog of ADHM construction
Abstract The ADHMN construction of selfdual Yang—Mills gauge fields is reformulated by introducing a functional space defined on a discrete point set. Using this formalism, a q -analogous object of the BPS monopole is obtained.
417374
Riemann–Liouville integrals of fractional order and extended KP hierarchy
An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann–Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators.
120480518
Exact Mass Spectrum for Non-Simply-Laced Affine Toda Solitons
Tha exact expression for the mass spectrum of solitons is found for imaginary coupling affine Toda theories associated with non-simply-laced loop algebra, dl~\ and cP>. It is calculated from exact field configuration. The obtained spectrum is contained in fundamental Toda particles in factorizable scattering theory as in the a\:!1 Toda case. Toda field theories have attracted much attention not only for their classical integrability but also for their connection to deformation problems of conformal field. theories.!) Of great interest in this class of theories is their algebraic structures. Various types of field equations classified by the Kac-Moody algebras have been vigorously investigated. 2 > A symmetry in the solution space associated with an infinite dimensional Lie algebra was found 2 > within the framework of field theories. Further, integrals of motion related to the quantum group symmetry have been studied, 3 > which reflect the W algebraic nature of the theories. It is well-known that there exist soliton type solutions to the two dimensional Toda lattice equation. 4 >,s> Affine theories are obtained by its reduction, in other words by imposing periodic constraint. One of the approach to investigate the algebraic structure of the system is to analyze properties of such exact solutions. It was shown by Hollowood 6 > that solitons in the imaginary coupling affine Toda field theory associated with a)~l type Kac-Moody algebra have energies of positive real values in spite of the complexity of the solutions. This fact is due to the symmetries of the a)~ I Dynkin diagram, i.e., the symmetries of the field equations. Other types of positive energy conditions 8 > were also considered, especially in the context of their superalgebra extensions. 7 > In this paper, we shall show exactly that the soliton energies in other affine theories, associated with dWr and c1 (l?::. 2) series, are also positive definite, though the solutions are complex. As in the d~1 cases, the resulting mass spectra are completely contained in those of fundamental Toda particles in the factorizable S-matrix theories. As mentioned above, the solitons in the affine theory can be obtained by reduction from the soliton solutions of infinite chain of two dimensional Toda field, of which equation of motion is written in the following form,
7321924
Magnetic solutions to 2 + 1 dimensional gravity with dilaton field
Abstract We show a general method to solve 2 + 1 dimensional dilatonic Maxwell-Einstein equation with a positive or negative cosmological constant. All the physical solutions are listed with assumptions that they are static, rotationally symmetric, and has a nonzero magnetic field and a nonzero dilaton field. On the contrary to the magnetic solution without a dilaton field, some of the present solutions with a dilaton field possess a horizon.
119092881
Condensation of Yang-Mills field at High Temperature in the Presence of Fermions
The possible condensation of the time-component of Yang-Mills field at finite temperature is discussed in the presence of Dirac fermions. We show that the condensation forms regardless of the number of fundamental and adjoint fermion species coupled to the Yang-Mills field. The effect of finite density of fermions is also investigated and it is shown that the magnitude of the condensation is also independent of the densities.
119274633
BORN-INFELD MONOPOLES AND INSTANTONS
We show that in certain non-Abelian Born-Infeld-Higgs theories there are monopole solutions obeying Bogomol’nyi-like equations in the PrasadSommerfield limit. We also discuss the existence of instanton solution in an SU(2) Born-Infeld theory. Upon a spontaneous breaking of gauge symmetry containing the SO(3) group, topologically stable configurations of gauge and scalar fields, known as “monopoles” may form [1]. The properties of the nonsingular objects, such as their masses, charges, and spins, have been closely investigated from the point of view of testing the grand unineation scheme. Besides the phenomenological characteristics, nathenatical methods for constructing the general monopole configurations have also been studied with much interest. The most interesting feature is the Bogomol’nyi equations [2] in the Prasad-Sommerfield limit [3]. The study of the Bogomol’nyi equations give not only the bound for monopole mass limit also the proof of existence of multi-monopole solutions [4]. The interaction among monopoles is very simplified when the Bogomol’nyi equations hold [5]. The first-order equations is also intimately related to study of supersymmetric systems [6]. Recently, the possibility that Yang-Mills interactions may receive correction at high energy region has been argued along with studying the string theory [7]. As a candidate for the modification, a generalized Born-Infeld (BI) action [8] instead of Yang-Mills action is preferred in effective field theories of open string theory [9]. The generalized-BI theory is expected to yield good behavior of its classical solution and wave propagation similarly to the original BI theory [10]. In our previous paper, we offered generalized (Abelian) Born-Infeld models in which there are self-dual vortex solutions [11]. In the present paper, we