Beyond Part III

Young Researchers in Mathematics 2009

16-18 April 2009

Centre for Mathematical Sciences, Cambridge

String Theory Session

Talks will be in MR9.



Phases of M2-brane Theories - Noppadol Mekareeya

We look at (2+1)-dimensional gauge theories arising from M2-branes probing toric Calabi-Yau (CY) singularities. There is an interesting phenomenon called Toric Duality, which corresponds to a situation in which one singular CY variety gives rise to more than one gauge theory (toric phase). Connections between toric phases will be discussed.

3-algebras in M-theory - Elena Mendez-Escobar

I will review the recent proposal of J. Bagger and N. Lambert for a low-energy effective field theory on a stack of coincident M2-branes focusing on a mathematical structure which is in the core of these theories: 3-algebras. In particular, I will explain what they are and how they can actually be written in terms of standard Lie algebras.

Pinched strings in the albelian Higgs model - Matthew Lake

We investigate static, noncylindrically symmetric solutions of the albelian Higgs field equations. In particular we propose a pinch solution which interpolates between degenerate vacuum states along the string, labelled by positive and negative n. This corresponds to a vortex which shrinks to a point and re emerges as an anti vortex resulting in the formation of a bead pair with one bead on either side of the intersection. We show that this solution is topologically stable and that the energy of the string core remains finite. Similarities between this solution and the extra dimensional windings of strings in type IIB string theory are also discussed and a correspondence between Higgs model and string theory parameters is suggested. The key result is an estimate of the mass of the Higgs boson in terms of the parameters which define the Klebanov Strassler geometry and which, in principle, may be tested by cosmological observations.

Using gauge/string duality to study QCD-like theories - Jerome Gaillard

The AdS/CFT correspondence is a strong-weak duality between string and gauge theories. One interesting application would be to study non-perturbative QCD. However, the best known example of the correspondence deals with N=4 Super-Yang-Mills, which is a supersymmetric theory of pure glue. This talks presents how to study QCD-like theories by breaking supersymmetry and adding flavors on the string theory side of the duality.

Pohlmeyer Reduction and the AdS/CFT correpsondence - Ben Hoare

Pohlmeyer Reduction of the classical 2d worldsheet sigma model arising from Type IIB superstring theory on AdS_5 x S^5 will be examined. In particular, its application to finding classical closed string solutions. Finally, there will be a discussion of the quantum properties of the Pohlmeyer reduced model.

Holography and string theory - Toby Wiseman (keynote speaker)

I will discuss the idea of `holography' in gravity, which states that in a quantum theory of gravity the number of degrees of freedom scale like the area of the boundary of the system, not as the volume as one might naively expect. I will introduce the `AdS-CFT' correspondence, which is a recent concrete realization of holography, where a quantum gravity theory is conjectured to be physically equivalent to a lower dimensional field theory. Implications for quantum gravity will be described.

Topology change in string theory - Rhys Davies

It has been demonstrated that the topology of spacetime can change in string theory. I will review the old work which establishes this for type II string theories, and discuss some of the differences which arise for the heterotic string.

Generalized Complex Geometry and String Theory - Hwasung Lee

Mirror symmetry relates type IIA string theories compactified on X with type IIB string theories compactified on the mirror Y. X and Y are related to each other in a non trivial way - in case of Calabi-Yaus the Euler numbers of X and Y have opposite signs, thus X and Y have different topology. Among the mirror symmetry formulation, we will be looking at the Strominger-Yau-Zaslow conjecture and discuss the generalization of it on generalized complex geometry framework. The talk will start from stating the SYZ conjecture, and introducing generalized complex geometry.

Heterotic Half-Flat Compactification - Cyril Matti

We briefly review heterotic flux compactification with the formalism of SU(3)-structure manifolds. Then, using the spinorial geometry techniques of [hep-th/0510176], we show how half-flat manifolds can be used for this compactification. This leads to the appearance of a new kind of geometrical flux creating a new superpotential in the effective 4d supergravity.

Metastable SUSY Breaking, de Sitter Moduli Stabilisation and Kähler Moduli Inflation - Sven Krippendorf

We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus direction. In more general compactifications with several Kahler moduli, we find a novel realisation of the LARGE volume scenario with D-term uplifting to de Sitter space and both D-term and F-term supersymmetry breaking. The structure of soft supersymmetry breaking terms is determined in the preferred scenario where the standard model cycle is not stabilised non-perturbatively and found to be flavour universal. Our scenario also provides a purely supersymmetric realisation of Kahler moduli (blow-up and fibre) inflation, with similar observational properties as the original proposals but without the need to include an extra (non-SUSY) uplifting term.

Holographic Hydrodynamics - Miguel Paulos

In this talk I review recent developments in computing hydrodynamic coefficients for strongly coupled gauge theories via the gauge-gravity duality. In particular I focus on finite (large) coupling corrections from higher derivative gravity theories.

Superstring Amplitudes and Stringy Signatures at the LHC (accessible talk) - Oliver Schlotterer

Superstring theory is only consistent in ten spacetime dimensions. Therefore, it has to be compactified down to four dimensions in order to make contact with the Standard Model. Using (super-)conformal field theory techniques, a set four-- and five--parton amplitudes including their cross sections have been constructed in the 4 d setting. A specific class of them exhibits universal properties independent on the the internal geometry of the six compactified dimensions. This is a big success for string theory's predictive power because in the context of string theory's "landscape problem", it is important to work out some common, model independent features of 4 d string vacua.

The parton amplitudes in question reproduce the Yang Mills result to leading order in the string lenght. From higher power corrections, one can e.g. derive some new contact interactions for gluons in the low energy effective action (proportional to fourth powers of the field strength). If the string scale is as low as the TeV range -- which is compatible with the high Planck scale in case of large extra dimensions -- the predicted four parton cross sections might be testable at the LHC in the near future.

This talk will give a brief introduction into the conformal field theory formalism applied to construct the amplitudes. I try to adjust the level of presentation to visitors of this year's Part III course "String Theory" by David Tong. The rest of the time will be spent on discussing the stringy results for amplitudes & cross sections and the comparison to Standard Model data.