ADE spectra in conformal field theory (original) (raw)
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We present an explicit construction, in terms of Fubini-Veneziano bosons, of the energy-momentum tensor, parafermionic primary fields and parafermionic operator product algebra for the FateevZamolodchikov-Gepner parafermionic conformal field theories. Other primary fields, including the spin fields and Zk neutral fields, are related to certain momentum states of these bosons. We also show that this bosonization is a special case of a more general construction which associates a Virasoro generator with every (ordered) pair (g, g') of simply-laced algebras.
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A minimal representation of a simple non-compact Lie group is obtained by "quantizing" the minimal nilpotent coadjoint orbit of its Lie algebra. It provides context for Roger Howe's notion of a reductive dual pair encountered recently in the description of global gauge symmetry of a (4-dimensional) conformal observable algebra. We give a pedagogical introduction to these notions and point out that physicists have been using both minimal representations and dual pairs without naming them and hence stand a chance to understand their theory and to profit from it.
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The target of the project is to understand and study the basics of Conformal Field Theory and how minimal models(In operator formalism) are important in many basic theories. In string theory conformal eld theory is also very important. Conformal Fields like bc CFT arises in bosonic string theory and CFT in supersymmetric string theory arises naturally when someone tries to quantize the string action. Thus quantize the bosonic strings. The project actually discusses the process of quantization of the bosonic strings and determine the dimension of the space-time using the anomaly cancellation.
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We propose a new q-series formula for a character of parafermion conformal field theories associated with arbitrary non-twisted affine Lie algebra ĝ. We show its natural origin from a thermodynamic Bethe Ansatz analysis including chemical potentials.
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The two major approaches to chiral conformal field theory -one based on operator algebras and one based on vertex algebras -both lead to representation categories which are tensor categories and, in the case of rational chiral conformal field theories, more specifically modular tensor categories. In this Arbeitsgemeinschaft, we have studied algebraic structures related to tensor categories arising in conformal field theory. The notion of a module category over this tensor category is central in the construction of a full local conformal field theory in various frameworks.
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Physics Letters B, 1993
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 ×(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 → 1 behaviour of all these fermionic sum representations to the thermodynamic Bethe Ansatz.