Past String Theory Seminar

After a review of the symmetries of supergravity theories and Kac-Moody

algebras, we explain show that M theory is likely to possess a very large

Kac-Moody symmetry of rank eleven, denoted by E_{11}. We also provide

evidence that even pure gravity and the closed bosonic string possess

analogous Kac-Moody symmetries.

Finally, we explain how the central charges of the maximal supergravity

theories arise naturally in E_{11}.

At the leading order, the low-energy effective field equations in string

theory admit solutions of the form of products of Minkowski spacetime and a

Ricci-flat Calabi-Yau space. The equations of motion receive corrections at

higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is

modified. In an appropriate choice of scheme, the Calabi-Yau space remains

Kahler, but is no longer Ricci-flat. We discuss the nature of these

corrections at order {\alpha'}^3, and consider the deformations of all the

known cohomogeneity one non-compact Kahler metrics in six and eight

dimensions. We do this by deriving the first-order equations associated with

the modified Killing-spinor conditions, and we thereby obtain the modified

supersymmetric solutions. We also give a detailed discussion of the boundary

terms for the Euler complex in six and eight dimensions, and apply the

results to all the cohomogeneity one examples. Additional material will be

presented concerning the case of holonomy G_2.

I present a calculation of the moduli Kahler potential for M-theory

on a G_2 manifold in a large radius approximation. The result is used to

analyze moduli dynamics and moduli stabilization in the context of the

associated four-dimensional effective theory.

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