Publication : t21/065

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 elds. Notably, the 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 compactied on T6. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional eld theory, nding in particular that the six-dimensional momenta do not correspond to a conventional spacetime section. When compactied on a circle, the sixdimensional multiplets give rise to the same degrees of freedom as ve-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies and the generation of Chern-Simons couplings, we nd reason to doubt that their dynamics will agree with the ve-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular xed-volume T3-bered spacetimes play a central role, suggesting that only on compactication 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 using the Batalin-Vilkovisky eld-antield formalism for any p and in arbitrary dimensions. Just as for the gravitino (p = 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.