Coset construction of logarithmic minimal models: branching rules and branching functions

Abstract

Working in the Virasoro picture, it is argued that the logarithmic minimal models LM(p,p')=LM(p,p';1) can be extended to an infinite hierarchy of logarithmic conformal field theories LM(p,p';n) at higher fusion levels n=1,2,3,.... From the lattice, these theories are constructed by fusing together n x n elementary faces of the appropriate LM(p,p') models. It is further argued that all of these logarithmic theories are realized as diagonal cosets (A_1^{(1)})_k \oplus (A_1^{(1)})_n / (A_1^{(1)})_{k+n} where n is the integer fusion level and k=np/(p'-p)-2 is a fractional level. These cosets mirror the cosets of the higher fusion level minimal models of the form M(m,m';n), but are associated with certain reducible representations. We present explicit branching rules for characters in the form of multiplication formulas arising in the logarithmic limit of the usual Goddard-Kent-Olive coset construction of the non-unitary minimal models M(m,m';n). The limiting branching functions play the role of Kac characters for the LM(p,p';n) theories.

16 pages, v2: footnote added

References in corpus (12)

• Logarithmic extensions of minimal models: characters and modular transformations
• Coset Constructions of Logarithmic (1,p)-Models
• Logarithmic CFTs connected with simple Lie algebras
• Integrable Boundary Conditions and W-Extended Fusion in the Logarithmic Minimal Models LM(1,p)
• W-Extended Logarithmic Minimal Models
• W-Extended Fusion Algebra of Critical Percolation
• Logarithmic Superconformal Minimal Models
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Coset construction of logarithmic minimal models: branching rules and branching functions
• Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
• SU(2)_k Logarithmic Conformal Field Theories
• A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule

Cited by in corpus (6)

• Logarithmic Superconformal Minimal Models
• Fusion hierarchies, T-systems and Y-systems of logarithmic minimal models
• Coset construction of logarithmic minimal models: branching rules and branching functions
• Fused RSOS Lattice Models as Higher-Level Nonunitary Minimal Cosets
• Kac boundary conditions of the logarithmic minimal models
• Staggered and affine Kac modules over $A_1^{(1)}$