Changrim Ahn

Fractional Supersymmetries in Perturbed Coset Cfts and Integrable Soliton Theory

Abstract We study integrable perturbations of the coset CFTs. The models are characterized by two fractional supersymmetries that are dual to each other. Generally, these models can be considered as restrictions of new integrable field theories we call fractional super soliton field theories. We study the connections with other models such as perturbations of WZW models, super sine-Gordon theory, Gross-Neveu models, and principal chiral models.

Complete S matrices of supersymmetric Sine-Gordon theory and perturbed superconformal minimal model

We derive the first complete S-matrices of the supersymmetric sine-Gordon theory for a general value of coupling constant. The spectrum includes not only solitons and antisolitons but also their bound states. The S-matrices are computed based on the soliton S-matrix which was obtained from the S-matrix of perturbed superconformal unitary model. After constructing a superconformal non-unitary model from the coset CFT with admissible representations, we derive the S-matrices of the perturbed superconformal non-unitary model by restricting the SSG S-matrices. We generalize these results to the theories with the fractional supersymmetries.

Onsager algebra and integrable lattice models

We derive many integrable lattice from the Ising and superintegrable chiral Potts models using the Onsager algebra. For each of these models, we also construct a class of integrable models from the automorphisms of the Onsager algebra. The extension of the Onsager algebra and associated intergrable models are considered.

String solutions in AdS_3 x S^3 x T^4 with NS-NS B-field

We develop an approach for solving the string equations of motion and Virasoro constraints in any background which has some (unfixed) number of commuting Killing vector fields. It is based on a specific ansatz for the string embedding. We apply the above mentioned approach for strings moving inAdS_3 x S^3 x T^4 with 2-form NS-NS B-field. We succeeded to find solutions for a large class of string configurations on this background. In particular, we derive dyonic giant magnon solutions in the R_t x S^3 subspace, and obtain the leading finite-size correction to the dispersion relation.

New parafermion, SU(2) coset and N = 2 superconformal field theories

In this paper we construct new parafermion theories, generalizing the ZL parafermion theory from integer L to rational L. These non-unitary parafermion theories (which are also defined as SL(2, R)L/U(1)) have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. We construct the string functions of these new parafermion theories. Generalizing Felders BRST cohomology approach we construct from the string functions the branching functions of the SU(2)L × SU(2)KSU(2)K+L coset theories, where both K, L are rational. New N = 2 superconformal field theories and topological field theories are also constructed. Their characters are obtained in terms of the new string functions.

Multi-matrix model and 2D Toda multi-component hierarchy

Abstract We study the integrability of the hermitian matrix-chain model at finite N . The integrable system, constructed from the matrix integrals using orthogonal polynomials is identified with the two-dimensional Toda system with multi-component hierarchy. We derive the Lax equations, the zero curvature conditions and an infinite number of conserved quantities for this 2D Toda hierarchy. The partition function of the matrix model is proved to be the “tau-function” of this Toda system. Also, using our formalism, we derive the Virasoro constraints on the partition function of the multi-matrix model for the first time.

Finite-size Giant Magnons on AdS_4 x CP^3_{\gamma}

We investigate finite-size giant magnons propagating on γ-deformed AdS4×CPγ3 type IIA string theory background, dual to one parameter deformation of the N=6 super Chern–Simons-matter theory. Analyzing the finite-size effect on the dispersion relation, we find that it is modified compared to the undeformed case, acquiring γ dependence.

RG flows of non-unitary minimal CFTs

Abstract In this paper we study the renormalization group flow of the ( p , q ) minimal (non-unitary) CFT perturbed by the Ф 1, 3 operator with a positive coupling. In the perturbative region q a (q-p) , we find a new IR fixed point which corresponds to the (2 p - q , p ) minimal CFT. The perturbing field near the new IR fixed point is identified with the irrelevant Ф 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 (2 p - q , p ) minimal CFT and the diagonal partition function into the diagonal.

One-point functions of loops and constraint equations of the multi-matrix models at finite N

Abstract 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. The interesting observation is that these generating operators of the one-point functions satisfy the W 1 + ∞ like algebra. Also, we obtain constraint equations on the partition functions in terms of the differential operators. These constraint equations on the partition function define the symmetries of the matrix models at an off-critical point before taking the double scaling limit.

RELATION BETWEEN YANG-BAXTER AND PAIR PROPAGATION EQUATIONS IN 16-VERTEX MODELS

We study the 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.