Integral cohomology of the Generalized Kummer fourfold

We describe the integral cohomology of the Generalized Kummer fourfold giving an explicit basis, using Hilbert scheme cohomology and tools developed by Hassett and Tschinkel. Then we apply our results to a IHS variety with singularities, obtained by a partial resolution of the Generalized Kummer quotiented by a symplectic involution. We calculate the Beauville--Bogomolov form of this new variety, presenting the first example of such a form that is odd.Comment: 40 pages, to appear in Algebraic Geometr

Self-Dual Tensors and Partial Supersymmetry Breaking in Five Dimensions

We study spontaneous supersymmetry breaking of five-dimensional supergravity theories from sixteen to eight supercharges in Minkowski vacua. This N=4 to N=2 breaking is induced by Abelian gaugings that require the introduction of self-dual tensor fields accompanying the vectors in the gravity multiplet and vector multiplets. These tensor fields have first-order kinetic terms and can become massive by a Stueckelberg-like mechanism. We identify the general class of N=2 vacua and show how the N=4 spectrum splits into massless and massive N=2 multiplets. In particular, we find a massive gravitino multiplet, containing two complex massive tensors, and a number of massive tensor multiplets and hypermultiplets. We determine the resulting N=2 effective action for the massless multiplets obtained by integrating out massive fields. We show that the metric and Chern-Simons terms of the vectors are corrected at one-loop by massive tensors as well as spin-1/2 and spin-3/2 fermions. These contributions are independent of the supersymmetry-breaking scale and thus have to be included at arbitrarily low energies.Comment: 33 page

Partial Supergravity Breaking and the Effective Action of Consistent Truncations

We study vacua of N = 4 half-maximal gauged supergravity in five dimensions and determine crucial properties of the effective theory around the vacuum. The main focus is on configurations with exactly two broken supersymmetries, since they frequently appear in consistent truncations of string theory and supergravity. Evaluating one-loop corrections to the Chern-Simons terms we find necessary conditions to ensure that a consistent truncation also gives rise to a proper effective action of an underlying more fundamental theory. To obtain concrete examples, we determine the N=4 action of M-theory on six-dimensional SU(2)-structure manifolds with background fluxes. Calabi-Yau threefolds with vanishing Euler number are examples of SU(2)-structure manifolds that yield N=2 Minkowski vacua. We find that that one-loop corrections to the Chern-Simons terms vanish trivially and thus do not impose constraints on identifying effective theories. This result is traced back to the absence of isometries on these geometries. Examples with isometries arise from type IIB supergravity on squashed Sasaki-Einstein manifolds. In this case the one-loop gauge Chern-Simons terms vanish due to non-trivial cancellations, while the one-loop gravitational Chern-Simons terms are non-zero.Comment: 44 pages, v2: minor changes, references adde

The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.Comment: 43 pages, 3 figure