Queen Mary, UL

In this talk I will be discussing some reformulations of string theory which promote T-duality to the level of a manifest symmetry namely Hull's Doubled Formalism and Klimcik and Severa's  Poisson-Lie T-duality.   Such formalisms double the number of fields but also incorporate some chirality-like constraint. Invoking this constraint leads one to consider sigma-models which, though duality invariant, do not possess manifest Lorentz Invariance.   Whilst such formalisms make sense at a classical level their quantum validity is less obvious.  I address this issue by examining the renormalization of these duality invariant sigma models.  This talk is based upon both forthcoming work and recent work in arXiv:0910.1345 [hep-th] and its antecedents arXiv:0708.2267, arXiv:0712.1121.

I discuss gauge theories for commutative but non-associative algebras

related to the SO(2k+1) covariant finite dimensional fuzzy 2k-sphere

algebras. A consequence of non-associativity is that gauge fields and

gauge parameters have to be generalized to be functions of coordinates as

well as derivatives. The usual gauge fields depending on coordinates only

are recovered after a partial gauge fixing.The deformation parameter for

these commutative but non-associative algebras is a scalar of the rotation

group. This suggests interesting string-inspired algebraic deformations of

spacetime which preserve Lorentz-invariance.

The talk will be based on hepth/0310153