Permutation orbifolds of supersymmetric minimal models

Abstract

In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N = 2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure relating various conformal field theories that seems not to be known in literature. Moreover, unexpected exceptional simple currents arise in the extended permuted models, coming from off-diagonal fields. In a few situations they admit fixed points that must be resolved. We determine the complete CFT data with all fixed point resolution matrices for all simple currents of all Z 2 -permutations orbifolds of all minimal N = 2 models with k = 2 mod 4. is the following. Start with a field f which has l-label equal to k 2 and apply J ± on f , recalling that J 4 ± = 1 and J 2 ± = T F for NS-type currents, f

The Kreuzer bi-homomorphism

“…Until recently, this was true only for tensor products of N = 2 minimal models. Recently, with my student Michele Maio [38], we succeeded in adding one more building block to this list, the Z 2 permutation orbifolds of two identical, already known building blocks.…”

Permutation-Twisted Modules for Even Order Cycles Acting on Tensor Product Vertex Operator Superalgebras

“…A theory of twisted operators for integral lattice vertex operator superalgebras and finite automorphisms that are lifts (in a certain way) of a lattice isometry were studied in [DL] and [X], and the general theory of twisted modules for vertex operator superalgebras was developed by Li in [Li]. Certain specific examples of permutation-twisted sectors in superconformal field theory have been studied from a physical point of view in, for instance, [FKS], [BHS], [MS1], [MS2].…”

Permutation orbifolds of heterotic Gepner models

“…The former has never been worked out for Kazama-Suzuki models, and the latter was not available for permutation orbifolds until last year. Using pioneering work by Borisov, Halpern and Schweigert [16] and an extension of these results to fixed point resolution matrices [17,18,19] we have constructed the Z 2 permutation orbifolds of N = 2 minimal models [20]. These can now be used as building blocks in heterotic CFT constructions, on equal footing, and in combination with all other building blocks, such as the minimal models themselves and free fermions.…”

“…• Check the consistency of the permutation orbifold CFTs we presented in [20]. Chiral heterotic spectra are very sensitive to the correctness of conformal weights and ground state dimensions of the CFT, as well as the correctness of the simple current orbits.…”

“…The key ingredient of the present work is is our previous paper [20], where we studied permutations, together with extensions in all possible order, and found very interesting novelties. For example, we determined how to construct a supersymmetric permutation of minimal models: in particular, the world-sheet-supersymmetry current in the supersymmetric orbifold turns out to be related to the anti-symmetric representation of the world-sheet-supersymmetry current of the original minimal model.…”