arXiv subjects
Publications and source records attributed to Martijn Wijnholt.
There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by means of a generalized Fourier-Mukai transform that relates spectral data to bundles over a rational surface fibration.
We consider the possibility of breaking the GUT group to the Standard Model gauge group in F-theory compactifications by turning on certain U(1) fluxes. We show that the requirement of massless hypercharge is equivalent to a topological constraint on the UV completion of the local model. The possibility of this mechanism is intrinsic to F-theory. We address some of the phenomenological signatures of this scenario. We show that our models predict monopoles as in conventional GUT models. We discuss in detail the leading threshold corrections to the gauge kinetic terms and their effect on unification. They turn out to be related to Ray-Singer torsion. We also discuss the issue of proton decay in F-theory models and explain how to engineer models which satisfy current experimental bounds.
We analyze M5-instantons in F-theory, or equivalently D3-instantons with varying axio-dilaton, in the presence of 7-brane gauge groups. The chiral two-form on the M5-brane plays an important role, because it couples the M5-brane to vector multiplets and charged chiral fields. The chiral two-form does not have a semi-classical description. However if the worldvolume of the M5 admits a fibration over a curve with surface fibers, then we can reduce the worldvolume theory to an `MSW' CFT by shrinking the surface. For this class of MSW instantons, we can use heterotic methods to do computations. We explain this in some detail using the physical gauge approach. We further compare M5-instantons with D3-instantons in perturbative type IIb and find some striking differences. In particular, we show that instanton zero modes tend to disappear and constraints from chirality on instanton contributions to the superpotential evaporate for finite string coupling.
We consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which specifies how the constituents of a configuration are glued together, but is usually assumed to be vanishing. Here we explain the rules for computing spectra and interactions for configurations with non-vanishing gluing VEVs. We further give a detailed discussion of the D-terms for Higgs bundles, spectral covers and ALE fibrations. We highlight a stability criterion that applies to degenerate configurations of the spectral data, and address an apparent discrepancy between the field theory and ALE descriptions. This allows us to show that one gets walls of marginal stability in F-theory even though they are absent in the 11d supergravity description. We also propose a numerical approach for approximating the hermitian-Einstein metric of the Higgs bundle using balanced metrics.
Despite much recent progress in model building with D-branes, it has been problematic to find a completely convincing explanation of gauge coupling unification. We extend the class of models by considering F-theory compactifications, which may incorporate unification more naturally. We explain how to derive the charged chiral spectrum and Yukawa couplings in N=1 compactifications of F-theory with G-flux. In a class of models which admit perturbative heterotic duals, we show that the F-theory and heterotic computations match.
String phenomenology is the branch of string theory concerned with making contact with particle physics. The original models involved compactifying ten-dimensional supersymmetric Yang-Mills theory on an internal Calabi-Yau three-fold. In recent years, this picture has been extended to compactifications of supersymmetric Yang-Mills theory in seven, eight or nine dimensions. We review some of this progress and explain the fundamental role played by Higgs bundles in this story.
Phenomenological compactifications of M-theory involve 7-manifolds with G_2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills theory on a three-manifold Q_3. We give a general discussion of compactifications of 7d Yang-Mills theory in terms of Higgs bundles on Q_3. We show they can be constructed using spectral covers, which are Lagrangian branes with a flat connection in the cotangent bundle T^*Q_3. We explain the dictionary with ALE fibrations over Q_3 and conjecture that these configurations have G_2 holonomy. We further develop tools to study the low energy effective theory of such a model. We show that the naive massless spectrum is corrected by instanton effects. Taking the instanton effects into account, we find that the massless spectrum and many of the interactions can be computed with Morse theoretic methods.
F-theory admits 7-branes with exceptional gauge symmetries, which can be compactified to give phenomenological four-dimensional GUT models. Here we study general supersymmetric compactifications of eight-dimensional Yang-Mills theory. They are mathematically described by meromorphic Higgs bundles, and therefore admit a spectral cover description. This allows us to give a rigorous and intrinsic construction of local models in F-theory. We use our results to prove a no-go theorem showing that local SU(5) models with three generations do not exist for generic moduli. However we show that three-generation models do exist on the Noether-Lefschetz locus. We explain how F-theory models can be mapped to non-perturbative orientifold models using a scaling limit proposed by Sen. Further we address the construction of global models that do not have heterotic duals. We show how one may obtain a contractible worldvolume with a two-cycle not inherited from the bulk, a necessary condition for implementing GUT breaking using fluxes. We also show that the complex structure moduli in global models can be arranged so that no dimension four or five proton decay can be generated.
This is a write-up of a two hour talk at the Simons workshop. It contains an elementary introduction to F-theory and may be useful for people new to the subject.
We exhibit a simple and robust mechanism for mediation of supersymmetry breaking between geometrically separated D-branes in type II string theory. The mediation proceeds via RR p-forms that couple via linear Chern-Simons terms to the abelian vector bosons on the branes. From a 4-d low energy perspective, the mechanism reduces to U(1) mediation.
The MSSM can arise as an orientifold of a pyramid-like quiver in the context of intersecting D-branes. Here we consider quiver realizations of the MSSM which can emerge at the bottom of a duality cascade. We classify all possible minimal ways this can be done by allowing only one extra node. It turns out that this requires extending the geometry of the pyramid to an octahedron. The MSSM at the bottom of the cascade arises in one of two possible ways, with the extra node disappearing either via Higgsing or confinement. Remarkably, the quiver of the Higgsing scenario turns out to be nothing but the quiver version of the left-right symmetric extension of the MSSM. In the minimal confining scenario the duality cascade can proceed if and only if there is exactly one up/down Higgs pair. Moreover, the symmetries of the octahedron naturally admit an automorphism of the quiver which solves a version of the mu problem precisely when there are an odd number of generations.
We explain how to construct a large class of new quiver gauge theories from branes at singularities by orientifolding and Higgsing old examples. The new models include the MSSM, decoupled from gravity, as well as some classic models of dynamical SUSY breaking. We also discuss topological criteria for unification.
We report on progress towards the construction of SM-like gauge theories on the world-volume of D-branes at a Calabi-Yau singularity. In particular, we work out the topological conditions on the embedding of the singularity inside a compact CY threefold, that select hypercharge as the only light U(1) gauge factor. We apply this insight to the proposed open string realization of the SM of hep-th/0508089, based on a D3-brane at a dP_8 singularity, and present a geometric construction of a compact Calabi-Yau threefold with all the required topological properties. We comment on the relevance of D-instantons to the breaking of global U(1) symmetries.
We show that Type IIB string theory on AdS_3 X S^3 X M_4 with p units of NS flux contains an integrable subsector, isomorphic to the minimal (p,1) bosonic string. To this end, we construct a topological string theory with target space Euclidean AdS_3 X S^3. We use a variant of Hamiltonian reduction to prove its equivalence to the minimal (p,1) string. The topological theory is then embedded in the physical ten-dimensional IIB string theory. Correlators of tachyons in the minimal string are mapped to correlators of spacetime chiral primaries in the IIB theory, in the presence of background 5-form RR flux. We also uncover a ground ring structure in AdS_3 X S^3 analogous to the well-known ground ring of the minimal string. This tractable model provides a literal incarnation of the idea that the holographic direction of AdS space is the Liouville field. We discuss a few generalizations, in particular we show that the N=4 topological string on an A_{p-1} ALE singularity also reduces to the (p,1) minimal string.
We motivate and apply a bottom-up approach to string phenomenology, which aims to construct the Standard Model as a decoupled world-volume theory on a D3-brane. As a concrete proposal for such a construction, we consider a single probe D3-brane on a partial resolution of a del Pezzo 8 singularity. The resulting world-volume theory reproduces the field content and interactions of the MSSM, however with a somewhat extended Higgs sector. An attractive feature of our approach is that the gauge and Yukawa couplings are dual to non-dynamical closed string modes, and are therefore tunable parameters.
In this paper we consider a somewhat unconventional approach for deriving worldvolume theories for D3 branes probing Calabi-Yau singularities. The strategy consists of extrapolating the calculation of F-terms to the large volume limit. This method circumvents the inherent limitations of more traditional approaches used for orbifold and toric singularities. We illustrate its usefulness by deriving quiver theories for D3 branes probing singularities where a Del Pezzo surface containing four, five or six exceptional curves collapses to zero size. In the latter two cases the superpotential depends explicitly on complex structure parameters. These are examples of probe theories for singularities which can currently not be computed by other means.
The matrix model computations of effective superpotential terms in N=1 supersymmetric gauge theories in four dimensions have been proposed to apply more generally to gauge theories in higher dimensions. We discuss aspects of five-dimensional gauge theory compactified on a circle, which leads to a unitary matrix model.
Curvature-squared corrections for D-brane actions in type II string theory were derived by Bachas, Bain and Green. Here we write down a generalisation of these corrections to all orders in $F$, the field strength of the U(1) gauge field on the brane. Some of these terms are needed to restore consistency with T-duality.