Mirror Mediation

I show that the effective action of string compactifications has a structure 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 Kahler 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 Kahler 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.Comment: 33 pages, 1 figure; v2: typos, references, minor correction

The QCD Axion and Moduli Stabilisation

We investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications. We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions. We observe that solving the F-term equations is insufficient for realistic moduli stabilisation and give a no-go theorem on supersymmetric moduli stabilisation with unfixed axions applicable to all string compactifications and relevant to much current work. We demonstrate how nonsupersymmetric moduli stabilisation with unfixed axions can be realised. We finally outline how to stabilise the moduli such that f_a is within the allowed window 10^9 GeV < f_a < 10^{12} GeV, with f_a ~ \sqrt{M_{SUSY} M_P}.Comment: 36 pages; v2: extended discussion of cosmological bound on f_a, references added, version accepted by journal; v3. factor of 2 correcte

The de Sitter swampland conjecture and supersymmetric AdS vacua

It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.Comment: Prepared for submission to Int. Journ. Mod. Phys. A; v2. added references and more discussio

On the Construction of Asymptotically Conical Calabi-Yau manifolds

This thesis is concerned with the construction of asymptotically conical (AC) Calabi-Yau manifolds. We provide an alternative proof of a result by Goto that states that the basic (p, 0)-Hodge numbers of a positive Sasaki manifold vanish for p > 0. Our main theorem then gives sufficient conditions on a non-compact Kähler manifold to admit an AC Calabi-Yau metric in each compactly supported Kähler class. As a corollary to this, we recover a result of van Coevering which guarantees the existence of an AC Calabi-Yau metric in each compactly supported Kähler class of a crepant resolution of a Calabi-Yau cone. It also follows that we are able to give sufficient conditions on a pair (X, D) , where X is a compact Kähler manifold and D is a divisor supporting the anti-canonical bundle of X, for X\D to admit an AC Calabi-Yau metric in each compactly supported Kähler class. We extend this last result to include cohomology classes in a specified subset of H2(X\D,R) containing the compactly supported Kähler classes. By imposing the condition h2, 0(X) = 0 on X, we can ensure that X\D contains an AC Calabi-Yau metric in every cohomology class in H2(X\D,R) that can be represented by a positive (1, 1)-form. This gives rise to new families of Ricci-flat Kähler metrics on certain non-compact Kähler manifolds. We furthermore construct AC Calabi-Yau metrics on smoothings of certain Calabi- Yau cones whose underlying complex space can be described by a complete intersection. As a consequence of the rate of convergence of these metrics to their asymptotic cone, we deduce from a theorem of Chan that any singular compact Calabi-Yau 3-fold with singularities modelled on the cubic [equation not reproduced here - see pdf of thesis], or on the complete intersection of two quadric cones in C⁵, both endowed with appropriate Ricci-flat metrics, admits a deformation. This last result is consistent with work of Gross