Multicharged dyonic integrable models

Abstract

We introduce and study new integrable models (IMs) of A (1) n -Non-Abelian Toda type which admit U(1) ⊗ U(1) charged topological solitons. They correspond to the symmetry breaking SU(n + 1) → SU(2) ⊗ SU(2) ⊗ U(1) n−2 and are conjectured to describe charged dyonic domain walls of N = 1 SU(n + 1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q = −1 member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well ) of the IMs of grades q = −1 and q = 2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n + 1) → SU(2) ⊗p ⊗ U(1) n−p as well as IM with global SU(2) symmetries are discussed. 1

Soliton Spectrum of Integrable Models with Local Symmetries

“…Again, by integrating the auxiliary fields A + ,Ā − , one gets (1.1). More explicitly the ungauged multicharged A (1) n (p = 2) IM is given by [23] L u p=2 = 1 2…”

“…We take eqn. (2.7) with g 0 ∈ G 0 = SL(2) ⊗ SL(2) ⊗ U(1) n−2 and A 0 = a 0 (z,z)(λ 1 + λ n ) · H,Ā 0 =ā 0 (z,z)(λ 1 + λ n ) · H, (a 0 ,ā 0 are arbitrary functions) and by performing the Gaussian integration over a 0 ,ā 0 we obtain the effective Lagrangian for the intermediate axial IM [23]…”

“…The result of the matrix Gaussian integration (over a 0a ,ā 0a , a = 1, n) is the following effective Lagrangian of the completely axialy gauged IM [23] L p=2…”

Higher grading conformal affine Toda theory and (generalized) sine-Gordon/massive Thirring duality

“…It has recently been shown that the sl(2) ATM model describes a confinement mechanism and the low-energy spectrum of QCD 2 (one flavor and N colors) [6]. Recently, some U (1) and U (1) x U (1) charged topological soliton solutions of certain class of affine Toda models have been interpreted as charged dyonic domain walls of 4D SU (N ) gauge theory and N = 1 SU (N ) SUSY gauge theory in the large N limit, respectively [9,10].…”

“…10) and the fact that e T F e −T = F + [T, F ] + ..., we have[F − q , bF + q b −1 ] = i{ α(l−q,i) m ψ α(l−q,i) ψ α(l−q,i) Lψ α(l−q,i) R exp − n α(l−q,i) b K ba ϕ a l α(l−q,i) c + α(q,i) m ψ α(q,i)ψ α(q,i) L ψ α(q,i) R exp n α(q,i) b K ba ϕ a l α(q,i) c }H 0 c (7.11)…”