Exact BPS monopole solution in a self-dual background
An exact one monopole solution in a uniform self-dual background field is obtained in the BPS limit of the SU(2) Yang-Mills-Higgs theory by using the inverse scattering method.
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arXiv subjects
Q-Han Park
Publications and source records attributed to Q-Han Park.
Field Theory for Coherent Optical Pulse Propagation
We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multi-level media. We show that the Bloch part of the equation can solved identically through $g$ and the remaining Maxwell equation becomes a second order differential equation with reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (nonabelian) symmetry structure of the Maxwell-Bloch equations for various multi-level media in association with symmetric spaces $G/H$. In particular, we associate nondegenerate two-level system for self-induced transparency with $G/H=SU(2)/U(1)$ and three-level $Ł$- or V-systems with $G/H = SU(3)/U(2)$. We give a detailed analysis for the two-level case in the matrix potential formalism, and address various new properties of the system including soliton numbers, effective potential energy, gauge and discrete symmetries, modified pulse area, conserved topological and nontopological charges. The nontopological charge measures the amount of self-detuning of each pulse. Its conservation law leads to a new type of pulse stability analysis which explains nicely earlier numerical results.
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Matched Pulse Propagation in a Three-Level System
The Bäcklund transformation for the three-level Maxwell-Bloch equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant electric field background, we obtain a general solution for matched pulses (a pair of solitary waves) which can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe. A nonlinear superposition rule is derived from the Bäcklund transformation and used for the explicit construction of two solitons as well as nonabelian breathers. Various new features of these solutions are addressed. In particular, we analyze in detail the scattering of "invertons", a specific pair of different wavelength solitons one of which moving with the velocity of light. Unlike the usual case of soliton scattering, the broader inverton changes its sign through the scattering. Surprisingly, the light velocity inverton receives time advance through the scattering thereby moving faster than light, which however does not violate causality.
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Path Integral Bosonization of Massive GNO Fermions
We show the quantum equivalence between certain symmetric space sine-Gordon models and the massive free fermions. In the massless limit, these fermions reduce to the free fermions introduced by Goddard, Nahm and Olive (GNO) in association with symmetric spaces $K/G$. A path integral formulation is given in terms of the Wess-Zumino-Witten action where the field variable $g$ takes value in the orthogonal, unitary, and symplectic representations of the group $G$ in the basis of the symmetric space. We show that, for example, such a path integral bosonization is possible when the symmetric spaces $K/G$ are $SU(N) \times SU(N)/SU(N); N \le 3, ~ Sp(2)/U(2)$ or $SO(8)/U(4)$. We also address the relation between massive GNO fermions and the nonabelian solitons, and explain the restriction imposed on the fermion mass matrix due to the integrability of the bosonic model.
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Self-Dual Chern-Simons Solitons and Generalized Heisenberg Ferromagnet Models
We consider the (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with the Chern-Simons gauge fields. Self-dual Chern-Simons solitons, the static zero energy solution saturating Bogomol'nyi bounds, are shown to exist when the generalized spin variable is valued in the Hermitian symmetric spaces G/H. By gauging the maximal torus subgroup of H, we obtain self-dual solitons which satisfy vortex-type nonlinear equations thereby extending the two dimensional instantons in a nontrivial way. An explicit example for the CP(N) case is given.
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Gravitational dressing of massive soliton theories
The massive soliton theories describe integrable perturbations of WZW cosets as generalized multi-component sine-Gordon models. We study their coupling to 2-dim gravity in the conformal gauge and show that the resulting models can be interpreted as conformal non-Abelian Toda theories when a certain algebraic condition is satisfied. These models, however, do not provide quantum mechanically consistent string backgrounds in the case the underlying WZW constraints are first solved classically.
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Scattering of Solitons in Derivative Nonlinear Schrödinger Model
We show that the chiral soliton model recently introduced by Aglietti et al. can be made integrable by adding an attractive potential with a fixed coefficient. The modified model is equivalent to the derivative nonlinear Schrödinger model which does not possess parity and Galilean invariance. We obtain explicit one and two classical soliton solutions and show that in the weak coupling limit, they correctly reproduce the bound state energy as well as the time delay of two-body quantum mechanics of the model.
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Nonabelian sine-Gordon theory and its application to nonlinear optics
Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A Lagrangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical applications, we show that they become precisely the effective field theories of self-induced transparency in nonlinear optics. This provides a dictionary between field theory and nonlinear optics.
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Effective Field Theory for Coherent Optical Pulse Propagation
Hidden nonabelian symmetries in nonlinear interactions of radiation with matter are clarified. In terms of a nonabelian potential variable, we construct an effective field theory of self-induced transparency, a phenomenon of lossless coherent pulse propagation, in association with Hermitian symmetric spaces $G/H$. Various new properties of self-induced transparency, e.g. soliton numbers, effective potential energy, gauge symmetry and discrete symmetries, modified pulse area, conserved $U(1)$-charge etc. are addressed and elaborated in the nondegenerate two-level case where $G/H = SU(2)/U(1)$. Using the $U(1)$-charge conservation, a new type of analysis on pulse stability is given which agrees with earlier numerical results.
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More on Generalized Heisenberg Ferromagnet Models
We generalize the integrable Heisenberg ferromagnet model according to each Hermitian symmetric spaces and address various new aspects of the generalized model. Using the first order formalism of generalized spins which are defined on the coadjoint orbits of arbitrary groups, we construct a Lagrangian of the generalized model from which we obtain the Hamiltonian structure explicitly in the case of $CP(N-1)$ orbit. The gauge equivalence between the generalized Heisenberg ferromagnet and the nonlinear Schrödinger models is given. Using the equivalence, we find infinitely many conserved integrals of both models.
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Gravitating BPS Dyons witout a Dilaton
We describe curved-space BPS dyon solutions, the ADM mass of which saturates the gravitational version of the Bogomol'nyi bound. This generalizes self-gravitating BPS monopole solutions of Gibbons et al. when there is no dilaton.
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Lagrangian Formulation of Symmetric Space sine-Gordon Models
The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim $σ$-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups $F \supset G \supset H$. We show that for every symmetric space $F/G$, the generalized sine-Gordon models can be derived from the $G/H$ WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.
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Complex sine-Gordon Theory for Coherent Optical Pulse Propagation
It is shown that the McCall-Hahn theory of self-induced transparency in coherent optical pulse propagation can be identified with the complex sine-Gordon theory in the sharp line limit. We reformulate the theory in terms of the deformed gauged Wess-Zumino-Witten sigma model and address various new aspects of self-induced transparency.
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Duality in Complex sine-Gordon Theory
New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant $\b > 0$ and the theory for $\b < 0$ is given which agrees with the Krammers-Wannier duality in the context of perturbed conformal field theory. The Bäcklund transform and the nonlinear superposition rule for the complex sine-Gordon theory are presented and from which, exact solutions, solitons and breathers with U(1) charge, are derived. We clarify topological and nontopological nature of neutral and charged solitons respectively, and discuss about the duality between the vector and the axial U(1) charges.
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Classical Matrix sine-Gordon Theory
The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the $A_{3}$-generalization where fields take value in $SU(2)$ describes integrable deformations of conformal field theory corresponding to the coset $SU(2) \times SU(2) /SU(2)$. Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and breathers which generalize those of the sine-Gordon theory with internal degrees of freedom, by applying the Zakharov-Shabat dressing method and explain their physical properties. Infinite current conservation laws and the Bäcklund transformation of the theory are obtained from the zero curvature formalism of the equation of motion. From the Bäcklund transformation, we also derive exact solutions as well as a nonlinear superposition principle by making use of the Bianchi's permutability theorem.
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An Effective Action for Quasi-elastic Scatterings in QCD
A new effective action for the high energy quark-quark scatterings is obtained by applying a scaling approximation to the QCD action. The propagators are shown to factorize into the transverse and the longitudinal parts so that the scattering amplitudes are given in terms of the products of two dimensional $S$-matrices. we show that our action provides a natural effective field theory for the Lipatov's theory of quark scatterings with quasi-elastic unitarity. The amplitude with quasi-elastic unitarity obtained from this action shows `Regge' behavior and is eikonalized.
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Massive Integrable Soliton Theories
Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the sine-Gordon and complex sine-Gordon theories. The fields of the theories take values in a non-abelian Lie group and it is argued that the coupling constant is quantized, unlike the situation in the sine-Gordon theory, which is a special case since its field takes values in an abelian group. It is further shown that these theories correspond to perturbations of certain coset conformal field theories. The solitons in the theories will, in general, carry non-abelian charges.
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Deformed Minimal Models and Generalized Toda Theory
We introduce a generalization of $A_{r}$-type Toda theory based on a non-abelian group G, which we call the $(A_{r},G)$-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine $(A_{1},SU(2))$-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator $Φ_{(2,1)}$. We derive infinite conserved charges and soliton solutions from the Lax pair of the affine $(A_{1}, SU(2))$-Toda theory. Another type of integrable deformation which accounts for the $Φ_{(3,1)}$-deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.
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