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Fermionic sum representations for conformal field theory characters. (English) Zbl 0973.81530

Summary: We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder construction. We also give fermionic representations for certain characters of the general \((G^{(1)})_k \times (G^{(1)})_l/(G^{(1)})_{k+l}\) coset conformal field theories, the non-unitary minimal models \(M(p, p+2)\) and \(M(p, kp+1)\), the \(N=2\) superconformal series, and the \(Z_N\)-parafermion theories, and relate the \(q\rightarrow 1\) behaviour of all these fermionic sum representations to the thermodynamic Bethe ansatz.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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