# Exotic supermultiplets in six dimensions : symmetries, quantisations and dynamics

Abstract : Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an N=(4,0) multiplet has a four index exotic graviton and it was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M theory compactified on T⁶. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional field theory, finding in particular that the six-dimensional momenta do not correspond to a conventional spacetime section. When compactified on a circle,the six-dimensional multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies and the generation of Chern-Simons couplings, we find reason to doubt that their dynamics will agree with the five-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular fixed-volume T³-fibered spacetimes play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity.In these exotic multiplets, there are also rank two antisymmetric tensor-spinors. In the last part of the thesis, we perform the quantisation of general antisymmetric tensor-spinors ψαμ1...μp using the Batalin-Vilkovisky field-antifield formalism for any ρ and in arbitrary dimensions. Just as for the gravitino (ρ=1), an extra propagating Nielsen-Kallosh ghost appears in quadratic gauges containing a differential operator. The appearance of this third ghost" is described within the BV formalism for arbitrary reducible gauge theories. We then use the resulting spectrum of ghosts and the Atiyah-Singer index theorem to compute gravitational anomalies.
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Submitted on : Wednesday, December 1, 2021 - 5:05:07 PM
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92429_ZHANG_2021_archivage.pdf
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• HAL Id : tel-03462284, version 1

### Citation

Yi Zhang. Exotic supermultiplets in six dimensions : symmetries, quantisations and dynamics. High Energy Physics - Theory [hep-th]. Université Paris-Saclay, 2021. English. ⟨NNT : 2021UPASP107⟩. ⟨tel-03462284⟩

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