Mon, 26 Oct 2009
12:00 -
13:00
L3
Gauge Threshold Corrections for Local String Models
Joe Conlon
(Oxford)
Abstract
Local string models are those where Standard Model degrees of freedom arise on a small region inside a large bulk volume. I study threshold effects on gauge coupling running for such models. The Kaplunovsky-Louis formula for locally supersymmetric gauge theories predicts the unification scale should be the bulk winding mode scale, parametrically large than the string scale where divergences are naively cut off. Analysis of explicit string models on orbifold/orientifold geometries confirms this; the winding mode scale arises from the presence of tadpoles uncancelled in the local model. I briefly discuss phenomenological applications to supersymmetry breaking and gauge coupling unification.
Mon, 19 Oct 2009
12:00 -
13:00
L3
A CY Manifold with 3 Generations and Small Hodge Numbers
Philip Candelas
(Oxford)
Abstract
I will discuss a Calabi-Yau manifold which admits free actions by Abelian and non-Abelian groups of order 12. The quotient manifolds have Euler number -6 and Hodge numbers (h^{11}, h^{21}) = (1,4). Apart from the various presentations of the Yau Manifold, that have Hodge numbers (6,9), this is the only other complete intersection CY manifold to admit a free quotient with Euler number -6 and hence three generations of particles with the standard embedding. I will discuss the spectrum of light particles and the possibility of a transgression to a heterotic vacuum on a manifold with Hodge numbers (2,2).
Thu, 03 Dec 2009
12:00 -
13:00
SR1
Moduli Spaces of Sheaves on Toric Varieties
Martijn Kool
(Oxford)
Abstract
Extending work of Klyachko, we give a combinatorial description of pure equivariant sheaves on a nonsingular projective toric variety X and construct moduli spaces of such sheaves. These moduli spaces are explicit and combinatorial in nature. Subsequently, we consider the moduli space M of all Gieseker stable sheaves on X and describe its fixed point locus in terms of the moduli spaces of pure equivariant sheaves on X. Using torus localisation, one can then compute topological invariants of M. We consider the case X=S is a toric surface and compute generating functions of Euler characteristics of M. In case of torsion free sheaves, one can study wall-crossing phenomena and in case of pure dimension 1 sheaves one can verify, in examples, a conjecture of Katz relating Donaldson--Thomas invariants and Gopakumar--Vafa invariants.
Thu, 26 Nov 2009
12:00 -
13:00
SR1
Introduction to self-duality and instantons
Ana Ferreira
(Oxford)
Abstract
We will present a self-contained introduction to gauge theory, self-duality and instanton moduli spaces. We will analyze in detail the situation of charge 1 instantons for the 4-sphere when the gauge group is SU(2). Time permitting, we will also mention the ADHM construction for k-instantons.