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Each solution may be interpreted as a classical vacuum of the second-quantized string field theory.
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The equations of constraint that arise from requiring a consistent first quantization of string theory (bosonic, supersymmetric, or heterotic) have an enormous number of solutions. The use of the constraint algebra to obtain the physical state conditions that the spectrum must satisfy is illustrated by an application to the massless states of the K = 4 fractional superstring. Issues concerning the associativity, modings and braiding properties of the fraction superconformal algebra are discussed. The form is derived of the fractional superconformal algebra appropriate for the tensor product theory that may generate the constraint algebra for the physical states of the fractional superstring. The representation of string theory is considered in which the Fock space is larger than the Lorentz-covariant one indicated by the fractional superstring partition function. Employing a bosonization of the parafermion theory, the author computes the operator product emission of the primary fields, and obtains the generalized commutation relations satisfied by the modes of these fields.
#Basic number theory review weil free
The K = 4 fractional superstring Fock space is constructed in terms of Z parafermions and free bosons. String theories are studied with world-sheet fraction supersymmetry, restricting the study to the SU(2), K = 4 case. It is shown how this method can more » be extended to study the irreducible representations of SU(N) minimal coset models (N>2), without detailed knowledge of the structures of the symmetry algebra. The author calculates the characters and branching functions of the irreducible representations and shows they agree with the known results for SU(2) coset models in the unitary case.
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It is shown that the SU(2) minimal coset conformal field theories have fractional supersymmetry by explicity constructing the irreducible representations of the algebra, employing a generalization of the BRST cohomology method introduced by Felder. These are generalizations of the ordinary superconformal algebra, which generate a symmetry between bosonic fields and parafermionic fields of fraction spin. The author studies the structure of the fractional superconformal algebras. We consider a benchmark bulk theory in four dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N0.