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Chaiho Rim

Publications and source records attributed to Chaiho Rim.

At least 73 records · Page 4Linked to original sources
arXiv2001

Reflection Amplitudes of Boundary Toda Theories and Thermodynamic Bethe Ansatz

We study the ultraviolet asymptotics in $A_n$ affine Toda theories with integrable boundary actions. The reflection amplitudes of non-affine Toda theories in the presence of conformal boundary actions have been obtained from the quantum mechanical reflections of the wave functional in the Weyl chamber and used for the quantization conditions and ground-state energies. We compare these results with the thermodynamic Bethe ansatz derived from both the bulk and (conjectured) boundary scattering amplitudes. The two independent approaches match very well and provide the non-perturbative checks of the boundary scattering amplitudes for Neumann and $(+)$ boundary conditions. Our results also confirm the conjectured boundary vacuum energies and the duality conjecture between the two boundary conditions.

hep-th↗
arXiv2001

Noncommutative field theory description of quantum Hall skyrmions

We revisit the quantum Hall system with no Zeeman splitting energy using the noncommutative field theory. We analyze the BPS condition for the delta-function interaction near the filling factor $ν=1$. Multi-skyrmions are shown to saturate the BPS bounds. The dimension of the moduli space of $k$ skyrmions is $4k+2$. Advantage of the noncommutative field description is demonstrated through the derivation of the effective nonlinear $σ$ model Lagrangian.

hep-th↗
arXiv2000

Reflection Amplitudes in Non-Simply Laced Toda Theories and Thermodynamic Bethe Ansatz

We study the ultraviolet asymptotics in non-simply laced affine Toda theories considering them as perturbed non-affine Toda theories, which possess the extended conformal symmetry. We calculate the reflection amplitudes, in non-affine Toda theories and use them to derive the quantization condition for the vacuum wave function, describing zero-mode dynamics. The solution of this quantization conditions for the ground state energy determines the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with Thermodynamic Bethe Ansatz(TBA) results. To make the comparison with TBA possible, we give the exact relations between parameters of the action and masses of particles as well as the bulk free energies for non-simply laced affine Toda theories.

hep-th↗
arXiv1999

Reflection Amplitudes of ADE Toda Theories and Thermodynamic Bethe Ansatz

We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with thermodynamic Bethe ansatz results.

hep-th↗
arXiv1999

Hidden Relation between Reflection Amplitudes and Thermodynamic Bethe Ansatz

In this paper we compute the scaling functions of the effective central charges for various quantum integrable models in a deep ultraviolet region $R\to 0$ using two independent methods. One is based on the ``reflection amplitudes'' of the (super-)Liouville field theory where the scaling functions are given by the conjugate momentum to the zero-modes. The conjugate momentum is quantized for the sinh-Gordon, the Bullough-Dodd, and the super sinh-Gordon models where the quantization conditions depend on the size $R$ of the system and the reflection amplitudes. The other method is to solve the standard thermodynamic Bethe ansatz (TBA) equations for the integrable models in a perturbative series of $1/(const. - \ln R)$. The constant factor which is not fixed in the lowest order computations can be identified {\it only when} we compare the higher order corrections with the quantization conditions. Numerical TBA analysis shows a perfect match for the scaling functions obtained by the first method. Our results show that these two methods are complementary to each other. While the reflection amplitudes are confirmed by the numerical TBA analysis, the analytic structures of the TBA equations become clear only when the reflection amplitudes are introduced.

hep-th↗
arXiv1998

Boundary Flows in general Coset Theories

In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the $SU(2)_{k}\otimes SU(2)_{l}/SU(2)_{k+l}$ coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion RSOS lattice models. For super CFTs ($k=2$) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we considered cover a wide class of integrable models. In particular, we show how the the impurity spin is screened by electrons for the $k$-channel Kondo model by taking $l\to\infty$ limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.

hep-th↗
arXiv1998

Soliton and Domain Wall in the Self-Dual CP(1) Model

We perform the dimensional reduction of the nonrelativistic CP(1) model coupled to an Abelian Chern-Simons gauge field in the self-dual limit, and investigate the soliton and domain wall solutions of the emerging 1+1 dimensional self-dual spin system. This system is described by inhomogeneous Landau-Lifshitz system with an extra non-local term. The Hamiltonian is Bogomol'nyi bounded from below and has four adjusting parameters. The Bogomol'nyi equation is described in detail in analogy with the Newtonian equation of motion and its numerical solution is presented.

hep-th↗
arXiv1997

Self-dual Chern-Simons Solitons in the Planar Ferromagnet

We consider a uniaxial planar ferromagnet coupled minimally to an Abelian Chern-Simons gauge field and study self-dual solitons which saturate the Bogomol'nyi bound. We find a rich structure of rotationally symmetric static soliton solutions for various uniform background charge densities. For a given ferromagnet material, the properties of these solitons are controlled only by the external magnetic field and the background charge.

hep-th↗
arXiv1997

A Self-Dual Bogomol'nyi Formulation of the Nonlinear Schrödinger Equation

We obtain a self-dual formulation of the conventional nonlinear Schrödinger equation (NLSE) in the 1+1 dimension by studying the dimensional reduction of the self-dual Chern-Simons nonlinear Schrödinger model (NLSM) in the 2+1 dimension. It is found that this self-dual formulation allows us to find not only the well-known soliton solutions from the Bogomol'nyi bound and the Galilean boost, but also other soliton solutions in the presence of the background sources.

hep-th↗
arXiv1996

Holstein-Primakoff Realizations on Coadjoint Orbits

We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the $SU(N+1)$ and $SU(1,N)$ group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a suitable normal ordering. The corresponding Dyson realizations are also obtained and some related issues are discussed.

hep-th↗
arXiv1996

On the $q$-deformed oscillator algebras:$su_q(1,1)$ and $su_q(2)$

We study the relations between $q$-deformations and $q$-coherent states of the single oscillator representations for $su_q(1,1)$ and $su_q(2)$ algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic oscilators. We also discuss the related Fock-Bargmann $q$-derivative and integration.

q-alg↗
arXiv1996

On the Three-Anyon Harmonics

The 3-anyon problem is studied using a set of variables recently proposed in an anyon gauge analysis by Mashkevich, Myrheim, Olaussen, and Rietman (MMOR). Boundary conditions to be satisfied by the wave functions in order to render the Hamiltonian self-adjoint are derived, and it is found that the boundary conditions adopted by MMOR are one of the ways to satisfy these general self-adjointness requirements. The possibility of scale-dependent boundary conditions is also investigated, in analogy with the corresponding analyses of the 2-anyon case. The structure of the known solutions of the 3-anyon in harmonic potential problem is discussed in terms of the MMOR variables. Within a series expansion in a boson gauge framework the problem of finding any anyon wavefunction is reduced to a (possibly infinite) set of algebraic equations, whose numerical analysis is proposed as an efficient way to study anyon physics.

hep-th↗
arXiv1995

Additional analytically exact solutions for three-anyons

We present new family of exact analytic solutions for three anyons in a harmonic potential (or in free space) in terms of generalized harmonics on $S^3$, which supplement the known solutions. The new solutions satisfy the hard-core condition when $α={1\over 3},1$ ($α$ being the statistical parameter) but otherwise, have finite non-vanishing two-particle colliding probability density, which is consistent with self-adjointness of the Hamiltonian. These solutions, however, do not have one-to-one mapping property between bosonic and fermionic spectra.

hep-th↗
arXiv1994

Effect of rotation symmetry to abelian Chern-Simons field theory and anyon equation on a sphere

We analyze the Chern-Simons field theory coupled to non-relativistic matter field on a sphere using canonical transformation on the fields with special attention to the role of the rotation symmetry: SO(3) invariance restricts the Hilbert space to the one with a definite number of charges and dictates Dirac quantization condition to the Chern-Simons coefficient, whereas SO(2) invariance does not. The corresponding Schrödinger equation for many anyons (and for multispecies) on the sphere are presented with appropriate boundary condition. In the presence of an external magnetic monopole source, the ground state solutions of anyons are compared with monopole harmonics. The role of the translation and modular symmetry on a torus is also expounded.

hep-th↗