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.
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.
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.
119039995
One-parameter family of selfdual solutions in classical Yang-Mills theory
Abstract The ADHM construction, which yields (anti-)selfdual configurations in classical Yang-Mills theories, is applied to an infinite dimensional l 2 vector space, and as a consequence, a family of (anti-)selfdual configurations with a parameter q is obtained for SU (2) Yang-Mills theory. This l 2 formulation can be seen as a q -analog of Nahm's monopole construction, so that the configuration approaches the BPS monopole at q →1 limit.
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.
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