Hypercharge Flux, Exotics, and Anomaly Cancellation in F-theory GUTs

We sharpen constraints related to hypercharge flux in F-theory GUTs that possess U(1) symmetries and argue that they arise as a consequence of 4-dimensional anomaly cancellation. This gives a physical explanation for all restrictions that were observed in spectral cover models while demonstrating that the phenomenological implications for a well-motivated set of models are not tied to any particular formalism.Comment: 5 pages; v2 published version: substantially revised (reordered some material, added discussion of MSSM gauge anomalies), references adde

Comments on Flipped SU(5) (and F-theory)

We study the impact of nonrenormalizable operators in flipped SU(5) that can generate a large mu term, R-parity violation, and rapid proton decay. While our motivation is to determine whether F-theory can naturally realize flipped SU(5), this analysis is general and leads to a characterization of symmetries capable of controlling such operators and should be independent of F-theory. We then discuss some specific implications for F-theory model building, where a significant mu problem is unavoidable. Finally, we mention previously noted difficulties associated to engineering GUT-Higgs fields in F-theory, suggest a direct engineering of SU(5) \times U(1)_{\chi} as an alternative, and present a sample construction of this type.Comment: 39 page

G_4 flux, chiral matter and singularity resolution in F-theory compactifications

We construct a set of chirality inducing G_4-fluxes in global F-theory compactifications on Calabi-Yau four-folds. Special emphasis is put on models with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model building, which are described in terms of a U(1)-restricted Tate model. In this type of constructions, the G_4-flux arises in a manner completely analogous to the U(1)_X gauge potential. We describe in detail the resolution by blow-up of the various singularities responsible for the U(1)_X factor and the standard SU(5) gauge group and match the result with techniques applied in the context of toric geometry. This provides an explicit identification of the structure of the resolved fibre over the matter curves and over the enhancement points relevant for Yukawa couplings. The U(1)_X flux induces a chiral matter spectrum. We compute the chiral index both of SU(5) charged matter and of SU(5) singlets charged only under U(1)_X localised on curves which are not contained in the SU(5) locus. We furthermore discuss global consistency conditions such as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation. The U(1)_X gauge flux is a global extension of a class of split spectral cover bundles. It constitutes an essential ingredient in the construction of globally defined F-theory compactifications with chiral matter. We exemplify this in a three-generation SU(5) x U(1)_X model whose flux satisfies all of the above global consistency conditions. We also extend our results to chiral fluxes in models without U(1) restriction.Comment: 53 pages, 2 figures; v2: details on Freed-Witten quantisation condition included, typos correcte

Fluxed M5-instantons in F-theory

We analyse the non-perturbative superpotential due to M5-brane instantons in F-theory compactifications on Calabi-Yau fourfolds. The M5 partition function is obtained via holomorphic factorisation by explicitly performing the sum over chiral 3-form fluxes. Comparison with the partition function of fluxed Euclidean D3-brane instantons in Type IIB orientifolds allows us to fix the spin structure on the intermediate Jacobian of the M5-instanton. We furthermore analyse the contribution of the M5-instanton to the superpotential in the presence of G4 gauge flux, where the superpotential is dressed with matter fields. We explicitly evaluate the pullback of G4 onto the M5-brane as a measure for the presence of charged instanton zero modes. This accounts for the M5 charge both under massless U(1)s, if present, and under what corresponds in Type II language to geometrically massive U(1)s.Comment: 47 pages. v3: refs. added, matches version published in Nuclear Physics

Towards the MSSM from F-theory

We study the MSSM in F-theory. Its group is the commutant to a structure group SU(5) x U(1)_Y of a gauge bundle in E_8. The spectrum contains three generations of quarks and leptons plus vectorlike electroweak and colored Higgses. The minimal MSSM Yukawa couplings with matter parity is obtained at the renormalizable level.Comment: 5 pages, 1 figure, published versio

Building SO(10) models from F-theory

We revisit local F-theory SO(10) and SU(5) GUTs and analyze their properties within the framework of the maximal underlying E_8 symmetry in the elliptic fibration. We consider the symmetry enhancements along the intersections of seven-branes with the GUT surface and study in detail the embedding of the abelian factors undergoing monodromies in the covering gauge groups. We combine flux data from the successive breaking of SO(10) to SU(5) gauge symmetry and subsequently to the Standard Model one, and further constrain the parameters determining the models' particle spectra. In order to eliminate dangerous baryon number violating operators we propose ways to construct matter parity like symmetries from intrinsic geometric origin. We study implementations of the resulting constrained scenario in specific examples obtained for a variety of monodromies.Comment: 53 page

Two loop partition function for large N pure Yang-Mills theory on a small three-sphere

We give a direct path-integral calculation of the partition function for pure 3+1 dimensional U(N) Yang-Mills theory at large N on a small three-sphere, up to two-loop order in perturbation theory. From this, we calculate the one-loop shift in the Hagedorn/deconfinement temperature for the theory at small volume, finding that it increases (in units of the inverse sphere radius) as we go to larger coupling (larger volume). Our results also allow us to read off the sum of one-loop anomalous dimensions for all operators with a given engineering dimension in planar Yang-Mills theory on R^4. As checks on our calculation, we reproduce both the Hagedorn shift and some of the anomalous dimension sums by independent methods using the results of hep-th/0412029 and hep-th/0408178. The success of our calculation provides a significant check of methods used in hep-th/0502149 to establish a first order deconfinement transition for pure Yang-Mills theory on a small three-sphere.Comment: 40 pages, 4 figures, harvma