The Weak Gravity Conjecture and Scalar Fields

We propose a generalisation of the Weak Gravity Conjecture in the presence of scalar fields. The proposal is guided by properties of extremal black holes in ${\cal N}=2$ supergravity, but can be understood more generally in terms of forbidding towers of stable gravitationally bound states. It amounts to the statement that there must exist a particle on which the gauge force acts more strongly than gravity and the scalar forces combined. We also propose that the scalar force itself should act on this particle stronger than gravity. This implies that generically the mass of this particle decreases exponentially as a function of the scalar field expectation value for super-Planckian variations, which is behaviour predicted by the Refined Swampland Conjecture. In the context of ${\cal N}=2$ supergravity the Weak Gravity Conjecture bound can be tied to bounds on scalar field distances in field space. Guided by this, we present a general proof that for any linear combination of moduli in any Calabi-Yau compactification of string theory the proper field distance grows at best logarithmically with the moduli values for super-Planckian distances.Comment: 25 pages. v2: Modified and extended section 4.1. v3: Clarifications added, published versio

On Natural Inflation and Moduli Stabilisation in String Theory

Natural inflation relies on the existence of an axion decay constant which is super-Planckian. In string theory only sub-Planckian axion decay constants have been found in any controlled regime. However in field theory it is possible to generate an enhanced super-Planckian decay constant by an appropriate aligned mixing between axions with individual sub-Planckian decay constants. We study the possibility of such a mechanism in string theory. In particular we construct a new realisation of an alignment scenario in type IIA string theory compactifications on a Calabi-Yau where the alignment is induced through fluxes. Within field theory the original decay constants are taken to be independent of the parameters which induce the alignment. In string theory however they are moduli dependent quantities and so interact gravitationally with the physics responsible for the mixing. We show that this gravitational effect of the fluxes on the moduli can precisely cancel any enhancement of the effective decay constant. This censorship of an effective super-Planckian decay constant depends on detailed properties of Calabi-Yau moduli spaces and occurs for all the examples and classes that we study. We expand these results to a general superpotential assuming only that the axion superpartners are fixed supersymmetrically and are able to show for a large class of Calabi-Yau manifolds, but not all, that the cancellation effect occurs and is independent of the superpotential. We also study simple models where the moduli are fixed non-supersymmetrically and find that similar cancellation behaviour can emerge. Finally we make some comments on a possible generalisation to axion monodromy inflation models.Comment: 24 pages. V2: Appendix on backreaction in axion monodromy added. References adde

Models of Particle Physics from Type IIB String Theory and F-theory: A Review

We review particle physics model building in type IIB string theory and F-theory. This is a region in the landscape where in principle many of the key ingredients required for a realistic model of particle physics can be combined successfully. We begin by reviewing moduli stabilisation within this framework and its implications for supersymmetry breaking. We then review model building tools and developments in the weakly coupled type IIB limit, for both local D3-branes at singularities and global models of intersecting D7-branes. Much of recent model building work has been in the strongly coupled regime of F-theory due to the presence of exceptional symmetries which allow for the construction of phenomenologically appealing Grand Unified Theories. We review both local and global F-theory model building starting from the fundamental concepts and tools regarding how the gauge group, matter sector and operators arise, and ranging to detailed phenomenological properties explored in the literature.Comment: 79 pages, Invited review article for the International Journal of Modern Physics

Towards large r from [p,q]-inflation

The recent discovery of B-mode polarizations in the CMB by the BICEP2 collaboration motivates the study of large-field inflation models which can naturally lead to significant tensor-to-scalar ratios. A class of such models in string theory are axion monodromy models, where the shift symmetry of an axion is broken by some branes. In type IIB string theory such models so far utilized NS5 branes which lead to a linear potential with an induced tensor-to-scalar ratio of $r \sim 0.07$. In this short note we study a modification of the scenario to include [p,q] 7-branes and show that this leads to an enhanced tensor-to-scalar ratio $r \sim 0.14$. Unlike 5-branes, 7-branes are in-principle compatible with supersymmetry, however we find that an implementation of the inflationary scenario requires an explicit breaking of supersymmetry by the 7-branes during inflation. This leads to similar challenges as in 5-brane models. We discuss the relation to high-scale supersymmetry breaking after inflation.Comment: 8 pp; v2: references added, typos correcte

On Gauge Threshold Corrections for Local IIB/F-theory GUTs

We study gauge threshold corrections for local GUT models in IIB/F-theory. Consistency with holomorphy requirements of supergravity and the Kaplunovsky-Louis formula implies that the unification scale is enhanced by the bulk radius R from the string scale to M_X =RM_S. We argue that the stringy interpretation of this is via a locally uncancelled tadpole sourced by the hypercharge flux. This sources closed string modes propagating into the bulk; equivalently open string gauge coupling running up to the winding scale M_X. The enhancement to R M_s is tied to GUT breaking by a globally trivial hypercharge flux and will occur in all models realising this mechanism.Comment: 4 pages; v2. journal versio

Vector-like exotics in F-theory and 750 GeV diphotons

AbstractThe recent excess in diphoton events around 750 GeV seen by the ATLAS and CMS experiments could be hinting at the existence of new vector-like charged matter around the TeV scale which couples to a singlet. Such a spectrum of exotics arises inevitably in certain classes of F-theory GUTs with hypercharge flux when the GUT symmetry is extended by a U(1) symmetry under which the Higgs fields of the MSSM are not vector-like. The exotics are not vector-like under the U(1) symmetry and therefore their mass is naturally related to its breaking scale. Previously this scale was taken to be close to the GUT scale which led to tension with proton decay, the μ-term magnitude, and too large R-parity violation. The 750 GeV excess provides new motivation for considering breaking the U(1) around the TeV scale, which additionally alleviates the previous problems. We study the possible TeV-scale spectrum in such an SU(5) GUT scenario and show that it is constrained and predictive. Gauge coupling unification can be retained at the accuracy of the MSSM at one loop even though typically the spectrum does not form complete GUT representations. For example the exotics cannot form a complete 10 multiplet but nonetheless happen to behave as one in the beta functions. We present an initial analysis of the diphoton production rates for the exotics spectra and find them compatible with data

Hypercharge Flux in IIB and F-theory: Anomalies and Gauge Coupling Unification

We analyse hypercharge flux GUT breaking in F-theory/Type IIB GUT models with regards to its implications for anomaly cancellation and gauge coupling unification. To this aim we exploit the Type IIB limit and consider 7-brane configurations that for the first time are guaranteed to exhibit net hypercharge flux restriction to matter curves. We show that local F-theory models with anomalies of type U(1)_Y-U(1)^2 in the massless spectrum can be consistent only if such additional U(1)s are globally geometrically massive (in the sense that they arise from non-Kahler deformations of the Calabi-Yau four-fold). Further, in such cases of geometrically massive U(1)s hypercharge flux can induce new anomalies of type U(1)_Y^2-U(1) in the massless spectrum, violating constraints in local models forbidding such anomalies. In particular this implies that it is possible to construct models exhibiting a U(1)_{PQ} global symmetry which have hypercharge flux doublet-triplet splitting and no further exotics. We also show that the known hypercharge flux induced splitting of the gauge couplings in IIB models at tree-level can be reduced by a factor of 5 by employing a more F-theoretic twisting of U(1) flux by hypercharge flux bringing it to well within MSSM 2-loop results. In the case of net restriction of hypercharge flux to matter curves this tree-level splitting becomes more involved, is tied to the vacuum expectation values of certain closed-string fields, and therefore gauge coupling unification becomes tied to the question of moduli stabilisation.Comment: 27 pages. v2: Expanded discussion on anomalies and showed that geometrically massive U(1)s of Peccei-Quinn type are compatible with hypercharge flux doublet-triplet splitting with no exotic