arXiv subjects

Changrim Ahn

Publications and source records attributed to Changrim Ahn.

84 records · Page 5Linked to original sources

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.

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arXiv1999

Quantisation of Conformal Fields in Three-dimensional Anti-de Sitter Black Hole Spacetime

Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 black hole spacetime should be absent. General argument establishing the absence of real particle creation by AdS_3 black hole spacetime for this case of conformal triviality is provided. Then next, using the explicit mode expansion forms for conformally-coupled scalar and spinor fields, the bosonic and fermionic superradiances are examined and found to be absent confirming the expectation.

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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.

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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.

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arXiv1996

Supersymmetric Sine-Gordon Model and the Eight-Vertex Free Fermion model with Boundary

We compute the boundary scattering amplitudes of the breathers of the supersymmetric sine-Gordon model using the fusion of the soliton-antisoliton pair scattering with the boundary with a known result of the soliton boundary scattering amplitudes. We also solve the boundary Yang-Baxter equation of the eight-vertex free fermion models to find the boundary reflection matrices. The former result is confirmed by the latter since the bulk $S$-matrices of the breathers can be identified with the trigonometric limit of the Boltzmann weights of the free fermion models. Our dual approach can answer a few quesions on the relationships between the free parameters in the boundary potential and those in the scattering amplitudes.

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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.

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arXiv1994

Relation between Yang-Baxter and Pair Propagation Equations in 16-Vertex Models

We study a relation between two integrability conditions, namely the Yang-Baxter and the pair propagation equations, in 2D lattice models. While the two are equivalent in the 8-vertex models, discrepancies appear in the 16-vertex models. As explicit examples, we find the exactly solvable 16-vertex models which do not satisfy the Yang-Baxter equations.

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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.

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arXiv1993

Thermodynamics and Form Factors of Supersymmetric Integrable Field Theories

We study on-shell and off-shell properties of the supersymmetric sinh-Gordon and perturbed SUSY Yang-Lee models using the thermodynamic Bethe ansatz and form factors. Identifying the supersymmetric models with the Eight Vertex Free Fermion Model, we derive inversion relation for inhomogeneous transfer matrix and TBA equations and get correct UV results. We obtain two-point form factors of the trace of energy-momentum tensor using the Watson equations and their SUSY transformations. As an application, we compute the UV central charge using these form factors and spectral representation of the $C$-theorem.

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arXiv1992

RG Flows of Non-Unitary Minimal CFTs

In this paper we study the renormalization group flow of the $(p,q)$ minimal (non-unitary) CFT perturbed by the $Φ_{1,3}$ operator with a positive coupling. In the perturbative region $q>>(q-p)$, we find a new IR fixed point which corresponds to the $(2p-q,p)$ minimal CFT. The perturbing field near the new IR fixed point is identified with the irrelevent $Φ_{3,1}$ operator. We extend this result to show that the non-diagonal ($(A,D)$-type) modular invariant partition function of the $(p,q)$ minimal CFT flows into the $(A,D)$-type partition function of the $(2p-q,p)$ minimal CFT and the diagonal partition function into the diagonal.

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arXiv1991

One-Point Functions of Loops and Constraints Equations of the Multi-Matrix Models at finite N

We derive one-point functions of the loop operators of Hermitian matrix-chain models at finite $N$ in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion relations from the Schwinger-Dyson equations. Interesting observation is that these generating operators of the one-point functions satisfy $W_{1+\infty}$-like algebra. Also, we obtain constraint equations on the partition functions in terms of the differential operators. These constraint equations on the partition functions define the symmetries of the matrix models at off-critical point before taking the double scaling limit.

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arXiv1991

Restricted sine-Gordon Theory in the Repulsive Regime as Perturbed Minimal CFTs

We construct the restricted sine-Gordon theory by truncating the sine-Gordon multi-soliton Hilbert space for the repulsive coupling constant due to the quantum group symmetry $SL_q(2)$ which we identify from the Korepin's $S$-matrices. We connect this restricted sine-Gordon theory with the minimal ($c<1$) conformal field theory ${\cal M}_{p/p+2}$ ($p$ odd) perturbed by the least relevent primary field $Φ_{1,3}$. The exact $S$-matrices are derived for the particle spectrum of a kink and neutral particles. As a consistency check, we compute the central charge of the restricted theory in the UV limit using the thermodynamic Bethe ansatz analysis and show that it is equal to that of ${\cal M}_{p/p+2}$.

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