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We study Abelian $S$-duality of Maxwell theory on $A$-type asymptotically locally Euclidean (ALE) spaces. Unlike on closed four-manifolds, the Maxwell path integral on an ALE space is not naturally a scalar partition function. Rather, it…

It is now well known that the moduli space of a vector bundle for heterotic string compactifications to four dimensions is parameterized by a set of sections of a weighted projective space bundle of a particular kind, known as Looijenga's…

We consider F-term hybrid inflation and supersymmetry breaking in the context of a model which largely respects a global U(1) R symmetry. The Kaehler potential parameterizes the Kaehler manifold with an enhanced U(1)x(SU(1,1)/U(1))…

The aim of this paper is to show the existence and give an explicit description of a pseudo-Riemannian metric and a symplectic form on the $\mathrm{S}\mathrm{L}(3,\mathbb{R})$-Hitchin component, both compatible with Labourie and Loftin's…

In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative integers p>=q such that p+q=N. Different choices of p and q, with N fixed,…

We continue our study of a general class of $\mathcal{N}=2$ supersymmetric $AdS_3\times Y_7$ and $AdS_2\times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively. The geometry of the internal spaces is part of a general family…

The first-order formulation of the G/K symmetric space sigma model of the scalar cosets of the supergravity theories is discussed when there is coupling of (m-1)-form matter fields. The Lie superalgebra which enables the dualized coset…

Let $H$ be an infinite-dimensional complex Hilbert space and let ${\mathcal G}_{\infty}(H)$ be the set of all closed subspaces of $H$ whose dimension and codimension both are infinite. We investigate (not necessarily surjective)…

Let $F$ be a local field with residue field $k$. The classifying space of $GL_n(F)$ comes canonically equipped with a map to the delooping of the $K$-theory space of $k$. Passing to loop spaces, such a map abstractly encodes a homotopy…

The analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally…

We construct a cohomological field theory for a gauged linear sigma model space in geometric phase, using the method of gauge theory and differential geometry. The cohomological field theory is expected to match the Gromov-Witten theory of…

We test the recently conjectured duality between $N=2$ supersymmetric type II and heterotic string models by analysing a class of higher dimensional interactions in the respective low-energy Lagrangians. These are $F$-terms of the form $F_g…

We establish sharp lower bounds for the mass of asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) toric 4-manifolds, in terms of equilibrium geometries consisting of gravitational instantons. More precisely, the…

We present novel realizations of E-model inflation within Supergravity which are largely associated with the existence of a pole of order one in the kinetic term of the (gauge-singlet) inflaton superfield. This pole arises due to the…

Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant…

We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure…

The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames…

Let $K\subset\R^d$ be compact and $A(K)$ the space of germs of real analytic functions on $K$ with its natural (LF)-topology. This topology can be given by $A(K)=\limind_{k\to+\infty} A_k$ where $A_k=\{(f_\alpha)_{\alpha\in\N_0^d}\in…

Affine Bruhat--Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of $\mathrm{PGL}$ parametrizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite-dimensional vector…

In differential geometry, geometric structures can often be encoded by differential forms satisfying algebraic and differential constraints. This is in particular the case for spinorial G-structures, where the defining tensors are…