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Some comments on symmetric orbifolds of K3

  • Roberto VolpatoEmail author
Open Access
Regular Article - Theoretical Physics
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Abstract

We consider two dimensional \( \mathcal{N} \) = (4, 4) superconformal field theories in the moduli space of symmetric orbifolds of K3. We complete a classification of the discrete groups of symmetries of these models, conditional to a series of assumptions and with certain restrictions. Furthermore, we provide a partial classification of the set of twining genera, encoding the action of a discrete symmetry g on a space of supersymmetric states in these models. These results suggest the existence of a number of surprising identities between seemingly different Borcherds products, representing Siegel modular forms of degree two and level N > 1. We also provide a critical review of various properties of the moduli space of these superconformal field theories, including the groups of dualities, the set of singular models and the locus of symmetric orbifold points, and describe some puzzles related to our (lack of) understanding of these properties.

Keywords

Conformal Field Theory Discrete Symmetries Sigma Models AdS-CFT Correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di Fisica e Astronomia ‘Galileo Galilei’ and INFN — Sezione di PadovaPadovaItaly

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