123682026
On a q-Analog of ADHMN Construction for Self-Dual Yang-Mills
Abstract It is known that many integrable systems can be reduced from self-dual Yang-Mills equations. The formal solution space to the self-dual Yang-Mills equations is given by the so called ADHM construction, in which the solution space are graded by vector spaces with dimensionality concerning topological index. When we consider a reduced self-dual system such as the Bogomol’nyi equations, in terms of ADHM construction, we need to incorporate an infinite dimensional vector space, in general. In this paper, we reformulate the ADHM construction by introducing various infinite dimensional vector spaces taking into account the reduction of self-dual system.
120649671
The Virasoro constraint and Hirota's bilinear difference equation
From the perspective of Hirota's bilinear difference equation, the connection of the tau function and the conformal symmetry is shown to become apparent and the Virasoro constraint is naturally derived. In this formalism, the compatibility of the flow provided by conformal symmetry and the KP flow is manifest.
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.
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.
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