New Orientifold Weak Coupling Limits in F-theory

We present new explicit constructions of weak coupling limits of F-theory generalizing Sen's construction to elliptic fibrations which are not necessary given in a Weierstrass form. These new constructions allow for an elegant derivation of several brane configurations that do not occur within the original framework of Sen's limit, or which would require complicated geometric tuning or break supersymmetry. Our approach is streamlined by first deriving a simple geometric interpretation of Sen's weak coupling limit. This leads to a natural way of organizing all such limits in terms of transitions from semistable to unstable singular fibers. These constructions provide a new playground for model builders as they enlarge the number of supersymmetric configurations that can be constructed in F-theory. We present several explicit examples for E8, E7 and E6 elliptic fibrations.Comment: 45 pages, typos correcte

Chern class identities from tadpole matching in type IIB and F-theory

In light of Sen's weak coupling limit of F-theory as a type IIB orientifold, the compatibility of the tadpole conditions leads to a non-trivial identity relating the Euler characteristics of an elliptically fibered Calabi-Yau fourfold and of certain related surfaces. We present the physical argument leading to the identity, and a mathematical derivation of a Chern class identity which confirms it, after taking into account singularities of the relevant loci. This identity of Chern classes holds in arbitrary dimension, and for varieties that are not necessarily Calabi-Yau. Singularities are essential in both the physics and the mathematics arguments: the tadpole relation may be interpreted as an identity involving stringy invariants of a singular hypersurface, and corrections for the presence of pinch-points. The mathematical discussion is streamlined by the use of Chern-Schwartz-MacPherson classes of singular varieties. We also show how the main identity may be obtained by applying `Verdier specialization' to suitable constructible functions.Comment: 26 pages, 1 figure, references added, typos correcte

On the renormalisability of gauge invariant extensions of the squared gauge potential

We show that gauge invariant extensions of the local functional \cO = \frac12\int d^4x A^2 have long range non localities which can only be ``renormalised'' with reference to a specific gauge. Consequently, there is no gauge independent way of claiming the perturbative renormalisability of these extensions. In particular, they are not renormalisable in the modern sense of Weinberg and Gomis. Critically, our study does not support the view that ghost fields play an indispensable role in the extension of a local operator into a non-local one as claimed recently in the literature.Comment: 1+13 pages. Revised version. New title and abstract. Extended introduction and several sentences have been inserted. Final version to appear in Physics Letters

Flopping and slicing: SO(4) and Spin(4)-models

We study the geometric engineering of gauge theories with gauge group Spin(4) and SO(4) using crepant resolutions of Weierstrass models. The corresponding elliptic fibrations realize a collision of singularities corresponding to two fibers with dual graphs A₁. There are eight different ways to engineer such collisions using decorated Kodaira fibers. The Mordell–Weil group of the elliptic fibration is required to be trivial for Spin(4) and ℤ/2ℤ for SO(4). Each of these models has two possible crepant resolutions connected by a flop. We also compute a generating function for the Euler characteristic of such elliptic fibrations over a base of arbitrary dimensions. In the case of a threefold, we also compute the triple intersection numbers of the fibral divisors. In the case of Calabi–Yau threefolds, we also compute their Hodge numbers and check the cancellations of anomalies in a six-dimensional supergravity theory

Singularities and Gauge Theory Phases

Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we present a correspondence between networks of small resolutions for singular elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge theories. While resolutions correspond to subchambers of the Coulomb branch, partial resolutions correspond to higher codimension loci at which the Coulomb branch intersects the Coulomb-Higgs branches. Flops between different resolutions are identified with reflections on the Coulomb branch. Physics aside, this correspondence provides an interesting link between elliptic fibrations and representation theory.Comment: 55 pages, 18 figures, section adde