Not doomed to fail

Anne Taormina,Katrin Wendland

doi:10.1007/jhep09(2018)062

Not doomed to fail

Anne Taormina, Katrin Wendland

Open Access

https://doi.org/10.1007/jhep09(2018)062

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Abstract

In their recent manuscript “An uplifting discussion of T-duality ” [26], J. Harvey and G. Moore have reevaluated a mod two condition appearing in asymmetric orbifold constructions as an obstruction to the description of certain symmetries of toroidal conformal field theories by means of automorphisms of the underlying charge lattice. The relevant “doomed to fail” condition determines whether or not such a lattice automorphism g may lift to a symmetry in the corresponding toroidal conformal field theory without introducing extra phases. If doomed to fail, then in some cases, the lift of g must have double the order of g. It is an interesting question, whether or not “geometric” symmetries are affected by these findings. In the present note, we answer this question in the negative, by means of elementary linear algebra: “geometric” symmetries of toroidal conformal field theories are not doomed to fail. Consequently, and in particular, the symmetry groups involved in symmetry surfing the moduli space of K3 theories do not differ from their lifts.

Highlights

JHEP09(2018)062 vectors.1 Both phenomena could potentially cast some doubt on traditional descriptions of symmetries in conformal field theory
In [9], we have shown that the maximal subgroup Z42 : A8 of M24 is the group which, by means of symmetry surfing, combines all geometric symmetries induced by the symmetries of complex tori in the corresponding Z2-orbifold conformal field theories
In this note we show that thanks to the very elegant “doomed to fail” condition, this question may be answered in the negative by means of elementary linear algebra: symmetry surfing is not doomed to fail by the uplifting properties of lattice automorphisms

Summary

Introduction

JHEP09(2018)062 vectors.1 Both phenomena could potentially cast some doubt on traditional descriptions of symmetries in conformal field theory. Moore have reevaluated a mod two condition appearing in asymmetric orbifold constructions as an obstruction to the description of certain symmetries of toroidal conformal field theories by means of automorphisms of the underlying charge lattice.

Results

Conclusion