scholarly journals New soliton solutions of anti-self-dual Yang-Mills equations

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Masashi Hamanaka ◽  
Shan-Chi Huang
Keyword(s):  
Gauge Group ◽  
Darboux Transformation ◽  
Domain Walls ◽  
Soliton Solutions ◽  
Real Space ◽  
Explicit Calculation ◽  
Yang Mills ◽  
Action Density ◽  
New Type ◽  
Exact Soliton Solutions

Abstract We study exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2) in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density TrFμνFμν can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group G = U(2) can be realized on our solition solutions or not is also discussed on each real space.

INTEGRABLE ASPECTS OF NONCOMMUTATIVE ANTI-SELF-DUAL YANG-MILLS EQUATIONS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2237-2238 ◽  
Author(s):  
MASASHI HAMANAKA
Keyword(s):  
Integrable Systems ◽  
Soliton Solutions ◽  
Bäcklund Transformations ◽  
Soliton Theory ◽  
Yang Mills ◽  
Backlund Transformations ◽  
Exact Soliton Solutions

We discuss extension of soliton theory and integrable systems to non-commutative (NC) spaces, focusing on integrable aspects of NC Anti-Self-Dual Yang-Mills (ASDYM) equations. We give exact soliton solutions (with both finite- and infinite-action solutions) by means of Bäcklund transformations. In the construction of NC soliton solutions, one kind of NC determinants, quasideterminants, play crucial roles. This is partially based on collaboration with C. R. Gilson and J. J. C. Nimmo (Glasgow).

scholarly journals Multi-soliton dynamics of anti-self-dual gauge fields

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Masashi Hamanaka ◽  
Shan-Chi Huang
Keyword(s):  
Phase Shift ◽  
Soliton Solution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Asymptotic Region ◽  
Principal Peak ◽  
Yang Mills ◽  
Action Density ◽  
Soliton Dynamics ◽  
Position Shift

Abstract We study dynamics of multi-soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2, ℂ) in four-dimensional spaces. The one-soliton solution can be interpreted as a codimension-one soliton in four-dimensional spaces because the principal peak of action density localizes on a three-dimensional hyperplane. We call it the soliton wall. We prove that in the asymptotic region, the n-soliton solution possesses n isolated localized lumps of action density, and interpret it as n intersecting soliton walls. More precisely, each action density lump is essentially the same as a soliton wall because it preserves its shape and “velocity” except for a position shift of principal peak in the scattering process. The position shift results from the nonlinear interactions of the multi-solitons and is called the phase shift. We calculate the phase shift factors explicitly and find that the action densities can be real-valued in three kind of signatures. Finally, we show that the gauge group can be G = SU(2) in the Ultrahyperbolic space 𝕌 (the split signature (+, +, −, −)). This implies that the intersecting soliton walls could be realized in all region in N=2 string theories. It is remarkable that quasideterminants dramatically simplify the calculations and proofs.

scholarly journals S-duality wall of SQCD from Toda braiding

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
B. Le Floch
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Domain Wall ◽  
Gauge Group ◽  
Domain Walls ◽  
Three Dimensional ◽  
Vertex Operators ◽  
Dual Operator ◽  
Yang Mills ◽  
Agt Correspondence

Abstract Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional $$ \mathcal{N} $$ N = 2 SU(N) SQCD with 2N hypermultiplets in terms of fields on the defect, namely three-dimensional $$ \mathcal{N} $$ N = 2 SQCD with gauge group U(N − 1) and 2N flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that T[SU(N)] (the S-duality wall of $$ \mathcal{N} $$ N = 4 super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a USp(2N − 2) gauge theory; it reduces to known results for N = 2. The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT.

scholarly journals Domain walls in 4d $$ \mathcal{N} $$ = 1 SYM

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Diego Delmastro ◽  
Jaume Gomis
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
Simons Theory ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Yang Mills ◽  
Stable Domain ◽  
Coxeter Number ◽  
Topological Quantum ◽  
Simply Connected

Abstract 4d$$ \mathcal{N} $$ N = 1 super Yang-Mills (SYM) with simply connected gauge group G has h gapped vacua arising from the spontaneously broken discrete R-symmetry, where h is the dual Coxeter number of G. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We put forward an explicit answer to this question for all the domain walls for G = SU(N), Sp(N), Spin(N) and G2, and for the minimal domain wall connecting neighboring vacua for arbitrary G. We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for SU(N). We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of SYM computed in the ultraviolet with those computed in our proposed infrared TQFTs. A crucial element in this matching is constructing the Hilbert space of spin TQFTs, that is, theories that depend on the spin structure of spacetime and admit fermionic states — a subject we delve into in some detail.

scholarly journals Darboux transformation for classical acoustic spectral problem

2003 ◽  
Vol 2003 (49) ◽  
pp. 3123-3142 ◽  
Author(s):  
A. A. Yurova ◽  
A. V. Yurov ◽  
M. Rudnev
Keyword(s):  
Spectral Problem ◽  
Inhomogeneous Medium ◽  
Darboux Transformation ◽  
Maxwell Equations ◽  
Soliton Solutions ◽  
Moutard Transformation ◽  
Acoustic Problem ◽  
Spatial Dimensions ◽  
Dielectric Permitivity ◽  
Harry Dym Equation

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a nonlinear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing-chain approach, we build a modified Harry Dym equation together with its LA pair. As an application, we construct some singular and nonsingular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.

Exact soliton solutions for the core of dispersion-managed solitons

2003 ◽  
Vol 68 (4) ◽  
Author(s):  
Zhiyong Xu ◽  
Lu Li ◽  
Zhonghao Li ◽  
Guosheng Zhou ◽  
K. Nakkeeran
Keyword(s):  
Soliton Solutions ◽  
The Core ◽  
Exact Soliton Solutions
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