arXiv subjects

Soonkeon Nam

Publications and source records attributed to Soonkeon Nam.

64 records · Page 4Linked to original sources

arXiv1996

Integrable structure in supersymmetric gauge theories with massive hypermultiplets

We study the quantum moduli space of vacua of $N=2$ supersymmetric $SU(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the fundamental representation. We identify the moduli space of the $N_c = 3$ and $N_f=2$ massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with {\it massive} quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of $N_{c}=3$ with $N_{f}=0, 1, 2$. We discuss possible generalizations of the integrable systems relevant to gauge theories with $N_c \neq 3 $ and general $N_f$.

hep-th↗

arXiv1995

Yangian Symmetries in the $SU(N)_1$ WZW Model and the Calogero-Sutherland Model

We study the $SU(N)$, level $1$ Wess-Zumino-Witten model, with affine primary fields as spinon fields of fundamental representation. By evaluating the action of the Yangian generators $Q_{0}^{a}, Q_{1}^{a}$ and the Hamiltonian $H_2$ on two spinon states we get a new connection between this conformal field theory and the Calogero-Sutherland model with $SU(N)$ spin. This connection clearly confirms the need for the $W_3$ generator in $H_2$ and an additional term in the $Q^{a}_{1}$. We also evaluate some energy spectra of $H_2$, by acting it on multi-spinon states.

hep-th↗

arXiv1995

Nonrelativistic Factorizable Scattering Theory of Multicomponent Calogero-Sutherland Model

We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable $S$-matrix theory with $SU(N)$-invariance. We find complete solutions of the Yang-Baxter equations without implementing the crossing symmetry, and one of them is identified with the scattering amplitudes derived from the Schrödinger equation of the Calogero-Sutherland model. This particular solution is of interest in that it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the $SU(N)$-invariant Yang-Baxter equations.

hep-th↗

arXiv1994

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.

hep-th↗

arXiv1994

Thermodynamics of Non-Relativistic Scattering Theory

We use thermodynamic Bethe ansatz to study nonrelativistic scattering theory of low energy excitations of 1D Hubbard model, using the $S$-matrices proposed by Eßler and Korepin. This model can be described by two types of excitation states, holons and spinons, as asymptotic states. In the attractive regime, the spinon is massive while the holon is massless. The situation is reversed with a repulsive coupling. We derive that the central charge of the Hubbard model in the IR limit is $c=1$ while it vanishes in the UV limit. The contribution is due to the massless degree of freedom, i.e. the holon for the attractive regime, and the massive mode decouples completely. This result is consistent with various known results based on lattice Bethe ansatz computations. Our results make it possible to use the $S$-matrices of the excitations to compute more interesting quantities like correlation functions.

hep-th↗

arXiv1993

Hamiltonian formulation of SL(3) Ur-KdV equation

We give a unified view of the relation between the $SL(2)$ KdV, the mKdV, and the Ur-KdV equations through the Fréchet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no non-local operators. We extend this method to the $SL(3)$ KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian structure of Ur-Bsq equationin a simple form. In particular, we explicitly construct the hamiltonian operator of the Ur-Bsq system which defines the poisson structure of the system, through the Fréchet derivative and its inverse.

hep-th↗

arXiv1993

Possible Tests of Conformal Turbulence through Boundaries

We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum $E(k)$ or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter $q$ appears explictly in the one point functions in the theory, which can also be tested.

hep-th↗

arXiv1993

Solutions of Conformal Turbulence on a Half Plane

Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tunning of coefficients. The simplest solution in our case is given by the minimal model of $p=2, q=33$ and moreover we find a fixed point of solutions when $p,q$ become large.

hep-th↗

arXiv1993

Classical $W_3^{(2)}$ algebra and its Miura map

We verify that the fractional KdV equation is a bi-hamiltonian system using the zero curvature equation in $SL(3)$ matrix valued Lax pair representation, and explicitly find the closed form for the hamiltonian operators of the system. The second hamiltonian operator is the classical version of the $W^{(2)}_3$ algebra. We also construct systematically the Miura map of $W^{(2)}_3$ algebra using a gauge transformation of the $SL(3)$ matrix valued Lax operator in a particular gauge, and construct the modified fractional KdV equaiotn as hamiltonian system.

hep-th↗

arXiv1993

Conformal Turbulence with Boundary

Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum confined in the upper half plane are obtained using the image method. This result enables us to address the infrared problem of the theory of conformal turbulence.

hep-th↗