Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group

The Kahler moduli space of a particular non-simply-connected Calabi-Yau manifold is mapped out using mirror symmetry. It is found that, for the model considered, the chiral ring may be identical for different associated conformal field theories. This ambiguity is explained in terms of both A-model and B-model language. It also provides an apparent counterexample to the global Torelli problem for Calabi-Yau threefolds.Comment: 12 page

The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study

The limiting procedure of special Kahler manifolds to their rigid limit is studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of certain singularities. In two examples we consider all the periods in and around the rigid limit, identifying the nontrivial ones in the limit as periods of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler potential of the special Kahler manifold reduces to that of a rigid special Kahler manifold. We extensively make use of the structure of these Calabi-Yau manifolds as K3 fibrations, which is useful to obtain the periods even before the K3 degenerates to an ALE manifold in the limit. We study various methods to calculate the periods and their properties. The development of these methods is an important step to obtain exact results from supergravity on Calabi-Yau manifolds.Comment: 79 pages, 8 figures. LaTeX; typos corrected, version to appear in Classical and Quantum Gravit

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi--Yau $d$-folds are somewhat different from the ``special K\"ahler manifolds'' which had occurred for $d=3$, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi--Yau manifolds. Our results agree with those obtained by more traditional mathematical methods in the limited number of cases for which the latter analysis can be carried out. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.Comment: 44 pages plus 3 tables using harvma

D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds

We study the space of geometric and open string moduli of type IIB compactifications from the perspective of complex structure deformations of F-theory. In order to find a correspondence, we work in the weak coupling limit and for simplicity focus on compactifications to 6 dimensions. Starting from the topology of D7-branes and O7-planes, we construct the 3-cycles of the F-theory threefold. We achieve complete agreement between the degrees of freedom of the Weierstrass model and the complex structure deformations of the elliptic Calabi-Yau. All relevant quantities are expressed in terms of the topology of the base space, allowing us to formulate our results for general base spaces.Comment: 40 pages, 15 figures, references adde

Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.Comment: 59 pages. Some changes in the references, a few minor points have been clarifie

Holomorphic Anomalies in Topological Field Theories

We study the stringy genus one partition function of $N=2$ SCFT's. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic curves over certain Calabi-Yau manifolds including the quintic threefold. This may be viewed as the first application of mirror symmetry at the string quantum level.Comment: 32 pages. Appendix by S.Kat

GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces

We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symmetry. We find that the Gr\"obner basis for the so-called toric ideal determines a finite set of differential operators for the local solutions of the GKZ system. At the special point called the large radius limit, we find a close relationship between the principal parts of the operators in the GKZ system and the intersection ring of a toric variety. As applications, we analyze general three dimensional hypersurfaces of Fermat and non-Fermat types with Hodge numbers up to $h^{1,1}=3$. We also find and analyze several non Landau-Ginzburg models which are related to singular models.Comment: 55 pages, 3 Postscript figures, harvma

Evidence for F(uzz) Theory

We show that in the decoupling limit of an F-theory compactification, the internal directions of the seven-branes must wrap a non-commutative four-cycle S. We introduce a general method for obtaining fuzzy geometric spaces via toric geometry, and develop tools for engineering four-dimensional GUT models from this non-commutative setup. We obtain the chiral matter content and Yukawa couplings, and show that the theory has a finite Kaluza-Klein spectrum. The value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points on the internal four-cycle S. This relation puts a non-trivial restriction on the space of gauge theories that can arise as a limit of F-theory. By viewing the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the geometry, we argue that this theory admits a holographic dual description in the large N limit. We also entertain the possibility of constructing string models with large fuzzy extra dimensions, but with a high scale for quantum gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde

Proceedings of the Salford Postgraduate Annual Research Conference (SPARC) 2011

These proceedings bring together a selection of papers from the 2011 Salford Postgraduate Annual Research Conference(SPARC). It includes papers from PhD students in the arts and social sciences, business, computing, science and engineering, education, environment, built environment and health sciences. Contributions from Salford researchers are published here alongside papers from students at the Universities of Anglia Ruskin, Birmingham City, Chester,De Montfort, Exeter, Leeds, Liverpool, Liverpool John Moores and Manchester

Cognitive behavioural therapy for thought disorder in psychosis

Clinicians are often sceptical about offering cognitive behavioural therapy (CBT) to individuals experiencing thought disorder. This view may result from perceived difficulties in clients being able to learn and better understand their experiences through verbal dialogue. However, it may also partly be due to the lack of clear guidance on how to address and work with these difficulties within therapy. This paper provides recommendations for delivering CBT in individuals experiencing thought disorder. It considers how clinicians might conduct their cognitive behavioural assessment, formulation, and intervention, targeting unhelpful appraisals and behaviour, and generating insight. The aim is to better disseminate the techniques sometimes applied in clinical practice