L3

Abstract: The alternative action for Yang-Mills theory, which Lionel Mason formulated in twistor space, explains some of the simplicities of gluon scattering amplitudes. We will review the derivation of the familiar CSW rules concerning tree-level scattering, show that the `missing' three-point amplitude can be correctly recovered and elucidate the connection with the canonical Lagrangian approach of Mansfied, Morris, et. al.

Abstract: We consider deformations of torsion-free $ G_2 $ structures, defined by the $ G_2 $-invariant 3-form $ \phi $ and compute the expansion of the Hodge star of $ \phi $ to fourth order in the deformations of $ \phi $. By considering M-theory compactified on a $ G_2 $ manifold, the $ G_2 $ moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $ \phi $ we work out the full curvature of this metric and relate it to the Yukawa coupling.

Abstract: We will discuss string $AdS_4$ domain wall solutions with stabilized moduli. These solutions are interesting, since they potentially induce decay processes between different vacua within the string landscape. Moreover, we discuss how black hole physics provide another tool of seeing through the vacuum landscape.

Abstract: We discuss the string-inspired approach to gauge theory amplitudes prompted by the work of Alday and Maldacena, in particular its application to weak coupling.

Abstract: Quantum Hall systems are characterized by a spectacular set of observations (universal low-temperature conductivity, critical behaviour and semi-circle laws for transitions between Quantum Hall states) that are more robust than would be expected from the detailed theory of underlying electron dynamics. The talk starts with a summary of these observations, and their derivation from the assumption that the important charge carriers at the low energies relevant to conductivity measurements are weakly interacting particles or vortices. This implies a large emergent duality symmetry (a level two subgroup of SL(2,Z)), whose presence underlies the robustness of the observations in question. The newly-discovered and unusual Quantum Hall properties of graphene are discussed as providing a new test of this picture.

Abstract: For a large class of compactifications of interest in string phenomenology, the task of finding vacua of the four dimensional effective theories can be rewritten as a simple problem in algebraic geometry. Using recent developments in computer algebra, the task can then be rapidly dealt with in a completely algorithmic fashion. I shall review the main points of hep-th/0606122 and hep-th/0703249 in which this approach to finding vacua was set out, before moving on to a description of the Mathematica package STRINGVACUA (as described in arXiv:0801.1508 [hep-th]). This package uses the power of the computer algebra system Singular and provides a user-friendly implementation of our methods, intended for use by physicists, within the comfortable working environment of Mathematica.

Abstract: I show that the effective action of string compactifications has astructure that can naturally solve the supersymmetric flavour and CP problems. At leading order in the $g_s$ and $\alpha'$ expansions, the hidden sector factorises. The moduli space splits into two mirror parts that depend on K\"ahler and complex structure moduli. Holomorphy implies the flavour structure of the Yukawa couplings arises in only one part. In type IIA string theory flavour arises through the K\"ahler moduli sector and in type IIB flavour arises through the complex structure moduli sector. This factorisation gives a simple solution to the supersymmetric flavour and CP problems: flavour physics is generated in one sector while supersymmetry is broken in the mirror sector. This mechanism does not require the presence of gauge, gaugino or anomaly mediation and is explicitly realised by phenomenological models of IIB flux compactifications.

Abstract: The moduli space of Calabi-Yau manifolds have a natural geometrical structure that has come to be known as special geometry. This geometry will be reviewed in the complex context and it will be shown that much of the structure persists for p-adic Calabi-Yau manifolds.

I will explain the connection between Shelah's recent notion of strongly dependent theories and finite weight in simple theories. The connecting notion of a strong theory is new, but implicit in Shelah's book. It is related to absence of the tree property of the second kind in a similar way as supersimplicity is related to simplicity and strong dependence to NIP.