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c=3d CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY

Satoru Odake

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Abstract

We define a superconformal algebra with the central charge c=3d, which is the symmetry of the non-linear σ model on a complex d dimensional Calabi-Yau manifold. The c=3d algebra is an extended superconformal algebra obtained by adding the spectral flow generators to the N=2 superconformal algebra. We study the representation theory and show that its representations are invariant under the integer-shift spectral flow. We present the character formulas and their modular transformation properties. We also discuss the relation to the N=4 superconformal algebra.

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We define a superconformal algebra with the central charge c=3d, which is the symmetry of the non-linear σ model on a complex d dimensional Calabi-Yau manifold. The c=3d algebra is an extended superconformal algebra obtained by adding the spectral flow generators to the N=2 superconformal algebra. We study the representation theory and show that its representations are invariant under the integer-shift spectral flow. We present the character formulas and their modular transformation properties. We also discuss the relation to the N=4 superconformal algebra.

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Available abstract

We define a superconformal algebra with the central charge c=3d, which is the symmetry of the non-linear σ model on a complex d dimensional Calabi-Yau manifold. The c=3d algebra is an extended superconformal algebra obtained by adding the spectral flow generators to the N=2 superconformal algebra. We study the representation theory and show that its representations are invariant under the integer-shift spectral flow. We present the character formulas and their modular transformation properties. We also discuss the relation to the N=4 superconformal algebra.

Key concepts: Superconformal algebra, Physics, Central charge, N = 2 superconformal algebra, Algebra representation, Virasoro algebra, Cellular algebra, Supersymmetry algebra

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