Related papers: Special Geometry and Automorphic Forms

We investigate a new 8-dimensional Riemannian geometry defined by a generic closed and coclosed 3-form with stabiliser PSU(3), and which arises as a critical point of Hitchin's variational principle. We give a Riemannian characterisation of…

We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by…

This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate…

We study the hypermultiplet moduli space of the type II string compactified on a Calabi-Yau space $\bX$. We do this by using IIA/IIB duality in a compactification of the same theory on $\bX\times \bS ^1$ and by using recent results on three…

Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, considered modulo isotopy. We introduce a moduli space D(G,S) and…

In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact K\"ahler manifold using analytic GIT theory. The aim of this article is to show that this classifying space taken in…

We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R^4. We identify global Darboux coordinates and quadratic Hamiltonians on…

We consider the general case of N=2 dual pairs of type IIA/heterotic string theories in four dimensions. We show that if the type IIA string in this pair can be viewed as having been compactified on a Calabi-Yau manifold in the usual way…

Type-IIB supersymmetric theories have an SL(2,Z) invariance, known as U-duality, which controls the non-perturbative behavior of the theory. Under SL(2,Z) the supercharges are doublets, implying that the bosonic charges would be singlets or…

We demonstrate that the moduli space of Hermitian-Einstein connections $\text{M}^*_{HE}(M^{2n})$ of vector bundles over compact non-Gauduchon Hermitian manifolds $(M^{2n}, g, \omega)$ that exhibit a dilaton field $\Phi$ admit a strong…

The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are…

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…

The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating…

We propose a construction of K\"ahler and non-K\"ahler Calabi-Yau manifolds by branched double covers of twistor spaces. In this construction we use the twistor spaces of four-manifolds with self-dual conformal structures, with the examples…

We study the action of mirror symmetry on two-dimensional N=(2,2) effective theories obtained by compactifying Type IIA string theory on Calabi-Yau fourfolds. Our focus is on fourfold geometries with non-trivial three-form cohomology. The…

We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2, R). The discrete spectrum is…

We study heterotic string compactifications on nearly K\"ahler homogeneous spaces, including the gauge field effects which arise at order \alpha'. Using Abelian gauge fields, we are able to solve the Bianchi identity and supersymmetry…

Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a…

We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional $\mathcal{N} =4$ super Yang-Mills theory on $\mathbb{CP}^{2}$ for the gauge group $SO(3)$ from the path integral of the effective…

We study exceptional algebroids in the context of warped compactifications of type IIA string theory down to $n$ dimensions, with $n\le 6$. In contrast to the M-theory and type IIB case, the relevant algebroids are no longer exact, and…