Integrable and conformal boundary conditions for Z(k) parafermions on a cylinder

We study integrable and conformal boundary conditions for � s�( 2) Zk parafermions on a cylinder. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with negative spectral parameter. The conformal boundary conditions labelled by (a, m) ∈ (G, Z2k) are identified with associated integrable lattice boundary conditions labelled by (r, a) ∈ (Ag−2 ,G )where g is the Coxeter number of the A-D-E graph G. We obtain analytically the boundary free energies, present general expressions for the parafermion cylinder partition functions and confirm these results by numerical calculations.

[1]  Zongan Qiu,et al.  Modular invariant partition functions for parafermionic field theories , 1987 .

[2]  Intertwiners and \ade Lattice Models , 1993, hep-th/9304009.

[3]  J.-B. Zuber,et al.  Generalised twisted partition functions , 2000 .

[4]  Surface free energies, interfacial tensions and correlation lengths of the ABF models , 1996, cond-mat/9607033.

[5]  M. .. Moore.  Exactly Solved Models in Statistical Mechanics , 1983 .

[6]  R. Baxter,et al.  Hard hexagons: exact solution , 1980 .

[7]  J.-B. Zuber,et al.  The many faces of Ocneanu cells , 2001 .

[8]  E. Verlinde,et al.  Fusion Rules and Modular Transformations in 2D Conformal Field Theory , 1988 .

[9]  J. Zuber,et al.  LETTER TO THE EDITOR: Integrable boundaries, conformal boundary conditions and A-D-E fusion rules , 1998, hep-th/9807142.

[10]  Integrable and Conformal Boundary Conditions for $$\widehat{s\ell}$$ (2) A–D–E Lattice Models and Unitary Minimal Conformal Field Theories , 2000, hep-th/0006094.

[11]  A. Sagnotti,et al.  Completeness conditions for boundary operators in 2D conformal field theory , 1996, hep-th/9603097.

[12]  Zongan Qiu,et al.  BRS cohomology and a Feigin-Fuchs representation of Kac-Moody and parafermionic theories , 1990 .

[13]  M. Jimbo,et al.  Free Field Construction for the ABF Models in Regime II , 2000 .

[14]  Boundary conditions in rational conformal field theories , 2000 .

[15]  P. Degiovanni.  Z/NZ Conformal Field Theories , 1990 .

[16]  J. Zuber,et al.  BCFT: From the boundary to the bulk , 2000, hep-th/0009219.

[17]  A. Nakayashiki,et al.  Crystalline Spinon Basis for RSOS Models , 1995, hep-th/9505083.

[18]  C. Itzykson,et al.  The A-D-E classification of minimal andA1(1) conformal invariant theories , 1987 .

[19]  P. Pearce,et al.  Conformal weights of RSOS lattice models and their fusion hierarchies , 1992 .

[20]  V. Fateev,et al.  Nonlocal (parafermion) currents in two-dimensional conformal quantum field theory and self-dual critical points in Z/sub N/-symmetric statistical systems , 1985 .

[21]  Melzer's identities revisited , 1998, math/9811156.

[22]  On New Conformal Field Theories with Affine Fusion Rules , 1999, hep-th/9901022.

[23]  Vincent Pasquier,et al.  Two-dimensional critical systems labelled by Dynkin diagrams , 1987 .

[24]  Roger E. Behrend,et al.  Integrable and Conformal Boundary Conditions for ŝ l ( 2 ) A – D – E Lattice Models and Unitary Minimal Conformal Field Theories , 2000 .

[25]  Alexander M. Polyakov,et al.  Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory , 1996 .

[26]  Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy , 1995, hep-th/9507118.

[27]  J. Zuber,et al.  On the classification of bulk and boundary conformal field theories , 1998, hep-th/9809097.