ON THE LANDAU–GINZBURG DESCRIPTION OF $(A_1^{(1)})^{\oplus N}$ INVARIANTS

Abstract

We search for a Landau-Ginzburg interpretation of non-diagonal modular invariants of tensor products of minimal n = 2 superconformal models, looking in particular at automorphism invariants and at some exceptional cases. For the former we find a simple description as Landau-Ginzburg orbifolds, which reproduce the correct chiral rings as well as the spectra of various Gepner-type models and orbifolds thereof. On the other hand, we are able to prove for one of the exceptional cases that this conformal field theory cannot be described by an orbifold of a Landau-Ginzburg model with respect to a manifest linear symmetry of its potential.

Counting charged massless states in the (0, 2) heterotic CFT/geometry connection

“…4 Discrete torsions can be interpreted as phase ambiguities of the orbifold group action on twisted vacua, which are proportional to α j because of the twist selection rules (also known as quantum symmetries [26]). In fact, the formula (2.5) was motivated by universalities observed in the classification efforts of [29] and the observation that proper account of quantum symmetries was vital for understanding the relation between orbifolds and modular invariants in Gepner models [30]. quantization (or generalized GSO) and the alignment of spinors with the Ramond sector, which we will discuss in turn.…”

“…30) for fields in the Ramond sector. Due to the triality of the Dynkin diagram of SO(8) the extension to SO(10) based on J GSO can be understood in terms of the alignment extension with a subsequent exchange of the characters V ↔ S of SO(8).…”

Where are the mirror manifolds?

“…The trouble is, however, that we do not know how to mod a quantum symmetry of a Calabi-Yau manifold. In the Landau-Ginzburg framework, on the other hand, where these symmetries usually are accessible by discrete torsion [20], it is not clear how to deform the model by moduli that are not polynomial deformations but come from twisted sectors.…”

“…It cannot be excluded that there exists some identification of the underlying conformal field theories, for example as an orbifold with respect to the non-linear Z Z 2 symmetry, but I do not know how to check for this possibility. Still, we can find some relation: As above, we can construct orbifold representations of the models in the invertible configurations C (1,1,12,16) [60] and C (1,1,8,20) [60] by cutting the loops. We can then deform the potentials such that they become the transpose of each other.…”

ADE string vacua with discrete torsion

“…This is, of course, independent of the torsions 6. These symmetries act only on the twisted sectors, with phases that are consistent with the orbifold selection rules[15]; they can be modded using discrete torsions (for examples see ref [22]…”