Triangle Seminars
Wednesday, 7 Nov 2012
On Singular Fibres in F-Theory
📍 London
Andreas Braun
(King's College)
Abstract:
In compactifications of M-Theory, certain singularities are expected to give rise to non-abelian gauge theories. In case the compactification manifold admits an torus fibration, such singularities become degenerations of the fibre. In this framework (which is called F-Theory), the behaviour of the fibre is well-understood for elliptic surfaces, but there remain puzzles both from the perspective of mathematics and physics in higher dimensions. After an introduction, I will report on some recent progress on the interplay of the structure of degenerate fibres and the effective field theory description.
In compactifications of M-Theory, certain singularities are expected to give rise to non-abelian gauge theories. In case the compactification manifold admits an torus fibration, such singularities become degenerations of the fibre. In this framework (which is called F-Theory), the behaviour of the fibre is well-understood for elliptic surfaces, but there remain puzzles both from the perspective of mathematics and physics in higher dimensions. After an introduction, I will report on some recent progress on the interplay of the structure of degenerate fibres and the effective field theory description.
Posted by: KCL
The AdS5xS5 string spectrum, Pohlmeyer reduction and quantum deformations
Stijn van Tongeren
(ITP and Spinoza Inst., Utrecht)
Abstract:
In the setting of integrability in AdS/CFT, in the typical approach to the AdS_5 x S^5 string a light-cone gauge is fixed, breaking Lorentz invariance on the worldsheet. One attempt to avoid the need for this goes under the name of Pohlmeyer reduction. Recently an S-matrix was conjectured to describe the scattering of solitons in this theory. Now as I will explain in my talk, the S-matrix of an integrable quantum field theory together with its dispersion relation are enough to find its finite volume spectrum exactly, through the so-called thermodynamic Bethe ansatz. I will work this out for an S-matrix and dispersion that interpolate between the standard light-cone gauge fixed superstring and this conjectured Pohlmeyer S-matrix, by analogy to a simpler model. Viewed as a deformation of the light-cone gauge fixed superstring TBA, this story is very similar to deforming the XXX spin chain to the XXZ one, which I will concretely discuss. I will finish by emphasizing important differences to this simple toy model, and discuss surprises in the so-called Y-system associated to the TBA equations.
In the setting of integrability in AdS/CFT, in the typical approach to the AdS_5 x S^5 string a light-cone gauge is fixed, breaking Lorentz invariance on the worldsheet. One attempt to avoid the need for this goes under the name of Pohlmeyer reduction. Recently an S-matrix was conjectured to describe the scattering of solitons in this theory. Now as I will explain in my talk, the S-matrix of an integrable quantum field theory together with its dispersion relation are enough to find its finite volume spectrum exactly, through the so-called thermodynamic Bethe ansatz. I will work this out for an S-matrix and dispersion that interpolate between the standard light-cone gauge fixed superstring and this conjectured Pohlmeyer S-matrix, by analogy to a simpler model. Viewed as a deformation of the light-cone gauge fixed superstring TBA, this story is very similar to deforming the XXX spin chain to the XXZ one, which I will concretely discuss. I will finish by emphasizing important differences to this simple toy model, and discuss surprises in the so-called Y-system associated to the TBA equations.
Posted by: IC