Abstract
By studying the infra-red fixed point of an $\mathcal{N}=(0,2)$ Landau-Ginzburg model, we find an example of modular invariant partition function beyond the ADE classification. This stems from the fact that a part of the left-moving sector is a new conformal field theory which is a variant of the parafermion model.
Highlights
A two-dimensional (2D) conformal field theory (CFT) is endowed with an infinite-dimensional Lie algebra [1], and modular invariance further constrains its spectrum on the torus [2]
A number of models have been exactly solved. (For instance, see [3].) In a rational conformal field theory, a modular invariant partition function consists of finitely many pairs I of left- and rightmoving characters of chiral algebras A ⊗ A, Z 1⁄4 X NiiχAi ⊗ χAi : ð1Þ
SU(2) and U(1), its modular invariant partition function fits into the ADE classification
Summary
A two-dimensional (2D) conformal field theory (CFT) is endowed with an infinite-dimensional Lie algebra [1], and modular invariance further constrains its spectrum on the torus [2]. (For instance, see [3].) In a rational conformal field theory, a modular invariant partition function consists of finitely many pairs I of left- and rightmoving characters of chiral algebras A ⊗ A,. −4 symmetry with ’t Hooft anomaly 27 These data suggest that, in the IR fixed point, the right-moving sector is the N 1⁄4 2 MM25 with level k 1⁄4 25, and the left-moving sector is the Uð1Þ27 WZNW model with level k 1⁄4 27=2 and a CFT of central charge. In the rightmoving sector that contribute to the elliptic genus, the state subject to L0 1⁄4 q=2 in the left-moving sector form the topological heterotic ring Htop [19,20] where q is equal to the Uð1ÞR charge rφ for a chiral field and rψ − 1 for a Fermi field. Þ∂ψ aψa ; ð6Þ and the operator product expansion (OPE) of a generator of Htop with the stress-energy tensor shows that it is a primary state with L0 1⁄4 J0=2
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