A new construction of Calabi–Yau manifolds: Generalized CICYs

We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi–Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a ‘configuration matrix’, a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi–Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi–Yau manifolds are complete intersections in (not necessarily Fano) ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.

Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

We consider SU(3)-equivariant dimensional reduction of Yang Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as Kahler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces. (C) 2015 The Authors. Published by Elsevier B.V.

N=4 supersymmetric AdS(5) vacua and their moduli spaces

We classify the N = 4 supersymmetric AdS(5) backgrounds that arise as solutions of five-dimensional N = 4 gauged supergravity. We express our results in terms of the allowed embedding tensor components and identify the structure of the associated gauge groups. We show that the moduli space of these AdS vacua is of the form SU(1, m)/ (U(1) x SU(m)) and discuss our results regarding holographically dual N = 2 SCFTs and their conformal manifolds.

Yang–Mills solutions and dyons on cylinders over coset spaces with Sasakian structure

We present solutions of the Yang–Mills equation on cylinders R×G/HR×G/H over coset spaces of odd dimension 2m+12m+1 with Sasakian structure. The gauge potential is assumed to be SU(m)SU(m)-equivariant, parameterized by two real, scalar-valued functions. Yang–Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in R2R2 under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang–Mills solutions that constitute SU(m)SU(m)-equivariant instanton configurations, we construct periodic sphaleron solutions on S1×G/HS1×G/H and dyon solutions on iR×G/HiR×G/H.