Past String Theory Seminar

27 April 2015
12:00
Philip Candelas
Abstract

Recently, as part of a project to find CY manifolds for which both the Hodge numbers (h^{11}, h^{21}) are small, manifolds have been found with Hodge numbers (4,1) and (1,1). The one-dimensional special geometries of their complex structures are more complicated than those previously studied. I will review these, emphasising the role of the fundamental period and Picard-Fuchs equation. Two arithmetic aspects arise: the first is the role of \zeta(3) in the monodromy matrices and the second is the fact, perhaps natural to a number theorist, that through a study of the CY manifolds over finite fields, modular functions can be associated to the singular manifolds of the family. This is a report on joint work with Volker Braun, Xenia de la Ossa and Duco van Straten.

  • String Theory Seminar
9 March 2015
12:00
Tudor Dimofte
Abstract
While the Higgs branch of a 3d N=4 gauge theory is protected from quantum corrections and its metric is easily computable, the Coulomb branch suffers both perturbative and nonperturbative corrections, and has long remained mysterious. I will present a construction of the Coulomb branch as a complex manifold, and (in principle) as a hyperkahler manifold. In particular, holomorphic functions on the Coulomb branch come from vevs of monopole operators in a chiral ring, and it turns out that this ring has a simple, quasi-abelian description. Applying the construction to linear quiver gauge theories, one finds new descriptions of singular monopole moduli spaces. I may also touch upon relations to equivariant vortex counting, geometric representation theory, and symplectic duality.
  • String Theory Seminar
2 March 2015
12:00
George Papadopoulos
Abstract

I shall demonstrate, under some mild assumptions, that the symmetry group of  extreme, Killing, supergravity horzions contains an sl(2, R) subalgebra.  The proof requires a generalization of the  Lichnerowicz theorem for non-metric connections. The techniques developed can also be applied in the classification
of AdS and Minkowski flux backgrounds.
 

  • String Theory Seminar
23 February 2015
12:00
Abstract
The spectrum of BPS states in four-dimensional gauge theories and string vacua with N=2 supersymmetry is well-known to be jump across certain walls in moduli space, where bound states can decay. In this talk I will survey how the discontinuity can be understood in terms of the supersymmetric quantum mechanics of mutually non-local point particles. This physical picture 
suggests that, at any point in moduli space, the BPS spectrum can be viewed as a sum of bound states of absolutely stable `single-centered' constituents. This idea appears to be vindicated in the context of quiver moduli spaces. Finally, I shall explain how the discontinuous BPS indices can be combined into a `new' supersymmetric index, a function which sums up multi-particle state contributions and is continuous across the wall.
  • String Theory Seminar
16 February 2015
12:00
Sakura Schafer-Nameki
Abstract

I will discuss how singular fibers in higher codimension in elliptically fibered Calabi-Yau fourfolds can be studied using Coulomb branch phases for d=3 supersymmetric gauge theories. This approach gives an elegent description of the generalized Kodaira fibers in terms of combinatorial/representation-theoretic objects called "box graphs", including the network of flops connecting distinct small resolutions. For physics applications, this approach can be used to constrain the possible matter spectra and possible U(1) charges (models with higher rank Mordell Weil group) for F-theory GUTs.

  • String Theory Seminar
9 February 2015
12:00
Charles Strickland-Constable
Abstract

Motivated by the study of supersymmetric backgrounds with non-trivial fluxes, we provide a formulation of supergravity in the language of generalised geometry, as first introduced by Hitchin, and its extensions. This description both dramatically simplifies the equations of the theory by making the hidden symmetries manifest, and writes the bosonic sector geometrically as a direct analogue of Einstein gravity. Further, a natural analogue of special holonomy manifolds emerges and coincides with the conditions for supersymmetric backgrounds with flux, thus formulating these systems as integrable geometric structures.
 

  • String Theory Seminar

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