O-folds. Orientifolds and orbifolds in exceptional field theory

Chris D A Blair,Daniel C Thompson,Emanuel Malek

doi:10.1007/jhep09(2018)157

Abstract

We describe conventional orientifold and orbifold quotients of string and M-theory in a unified approach based on exceptional field theory (ExFT). Using an extended spacetime, ExFT combines all the maximal ten and eleven dimensional supergravities into a single theory manifesting a global symmetry corresponding to the exceptional series of Lie groups. Here we will see how this extends to half-maximal theories by showing how a single ℤ2generalised orbifold (or O-fold), of ExFT gives rise to M-theory on an interval, type II with orientifold planes and the heterotic theories in an elegant fashion. We study in more detail such orbifold and orientifold actions preserving half-maximal supersymmetry, and show how the half-maximal structure of ExFT permits the inclusion of localised non-Abelian vector multiplets located at the orbifold fixed points. This allows us to reproduce for the ℤ2 example the expected modifications to the gauge transformations, Bianchi identities and actions of the theories obtained from the single ExFT starting point. We comment on the prospects of studying anomaly cancellation and more complicated, non-perturbative O-folds in the ExFT framework.

Highlights

Despite substantial effort during the 23 years since the inception of M-theory [1], it remains an open problem to provide a complete account of the theory beyond its low energy limits or its perturbative vacua described by critical superstring theories
We describe conventional orientifold and orbifold quotients of string and Mtheory in a unified approach based on exceptional field theory (ExFT)
We study in more detail such orbifold and orientifold actions preserving half-maximal supersymmetry, and show how the half-maximal structure of ExFT permits the inclusion of localised non-Abelian vector multiplets located at the orbifold fixed points

Summary

Introduction

Despite substantial effort during the 23 years since the inception of M-theory [1], it remains an open problem to provide a complete account of the theory beyond its low energy limits or its perturbative vacua described by critical superstring theories. A significant enterprise has been to develop a theory that captures the low energy effective dynamics of M-theory i.e. supergravity, but in way that promotes dualities to manifest symmetries This approach has centred on the development of double field theory (DFT) [5,6,7] and exceptional field theory (ExFT) [8, 9]. These theories provide linear realisations of O(d − 1, d − 1) (T-duality) or Ed(d) (U-duality) acting on an extended space obtained by augmenting the coordinates of the regular maximal supergravity theories with additional spatial coordinates. We must impose a constraint on the coordinate dependence, which restricts the total number of “physical” coordinates, on which fields can depend, to 10 or 11

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Conclusion