Boundary conformal field theory and fusion ring representations
Jun, 2001Citations per year
Abstract:
To an RCFT corresponds two combinatorial structures: the amplitude of a torus (the 1-loop partition function of a closed string, sometimes called a modular invariant), and a representation of the fusion ring (called a NIM-rep or equivalently a fusion graph, and closely related to the 1-loop partition function of an open string). In this paper we develop some basic theory of NIM-reps, obtain several new NIM-rep classifications, and compare them with the corresponding modular invariant classifications. Among other things, we make the following fairly disturbing observation: there are infinitely many (WZW) modular invariants which do not correspond to any NIM-rep. The resolution could be that those modular invariants are physically sick. Is classifying modular invariants really the right thing to do? For current algebras, the answer seems to be: Usually but not always. For finite groups a la Dijkgraaf-Vafa-Verlinde-Verlinde, the answer seems to be: Rarely.Note:
- 58 pages, 4 figures Subj-class: High Energy Physics - Theory: Quantum Algebra
- 11.25.Hf
- 02.20.Sv
- field theory: conformal
- field theory: rational
- dimension: 2
- boundary condition
- algebra: fusion
- invariance: modular
- partition function
- perturbation theory: higher-order
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