TY - JOUR

T1 - Applications of reflection amplitudes in Toda-type theories

AU - Ahn, Changrim

AU - Kim, Chanju

AU - Rim, Chaiho

N1 - Funding Information:
We thank P. Baseilhac and V. Fateev for fruitful collaborations and F. Smirnov and Al. Zamolodchikov for valuable discussions. This work is supported in part by KRF-99-015-DI0021, MOST 98-N6-01-01-A-05 (CA), and KOSEF 1999-2-112-001-5(CA,CR).

PY - 2001/2

Y1 - 2001/2

N2 - Reflection amplitudes are defined as two-point functions of certain class of conformal field theories where primary fields are given by vertex operators with real couplings. Among these, we consider (Super-) Liouville theory and simply and non-simply laced Toda theories. In this paper we show how to compute the scaling functions of effective central charge for the models perturbed by some primary fields which maintains integrability. This new derivation of the scaling functions are compared with the results from conventional TBA approach and confirms our approach along with other non-perturbative results such as exact expressions of the on-shell masses in terms of the parameters in the action, exact free energies. Another important application of the reflection amplitudes is a computation of one-point functions for the integrable models. Introducing functional relations between the one-point functions in terms of the reflection amplitudes, we obtain explicit expressions for simply-laced and non-simply-laced affine Toda theories. These nonperturbative results are confirmed numerically by comparing the free energies from the scaling functions with exact expressions we obtain from the one-point functions.

AB - Reflection amplitudes are defined as two-point functions of certain class of conformal field theories where primary fields are given by vertex operators with real couplings. Among these, we consider (Super-) Liouville theory and simply and non-simply laced Toda theories. In this paper we show how to compute the scaling functions of effective central charge for the models perturbed by some primary fields which maintains integrability. This new derivation of the scaling functions are compared with the results from conventional TBA approach and confirms our approach along with other non-perturbative results such as exact expressions of the on-shell masses in terms of the parameters in the action, exact free energies. Another important application of the reflection amplitudes is a computation of one-point functions for the integrable models. Introducing functional relations between the one-point functions in terms of the reflection amplitudes, we obtain explicit expressions for simply-laced and non-simply-laced affine Toda theories. These nonperturbative results are confirmed numerically by comparing the free energies from the scaling functions with exact expressions we obtain from the one-point functions.

KW - Affine Toda field theory

KW - Conformal field theory

KW - One-point function

KW - Reflection amplitude

KW - Super-Liouville theory

KW - Thermodynamic Bethe Ansatz

UR - http://www.scopus.com/inward/record.url?scp=0035255921&partnerID=8YFLogxK

U2 - 10.1023/A:1004826214195

DO - 10.1023/A:1004826214195

M3 - Article

AN - SCOPUS:0035255921

SN - 0022-4715

VL - 102

SP - 385

EP - 419

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3-4

ER -