Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry

F-theory GUTs provide a promising UV completion for models with approximate gauge coupling unification, such as the (non-supersymmetric) Standard Model. More specifically, if the superparters have masses well above the TeV scale, the resulting imperfection in unification can be accounted for by the, in principle calculable, classical F-theory correction at the high scale. In this paper we argue for the correct form of the F-theory corrections to unification, including KK mode loop effects. However, the price of compensating the imprecise unification in such High Scale SUSY models with F-theory corrections is that the GUT scale is lowered, potentially leading to a dangerously high proton decay rate from dimension-6 operators. We analyse the possibility of suppressing the decay rate by the localization of $X,Y$ gauge bosons in higher dimensions. While this effect can be very strong for the zero modes, we find that in the simplest models of this type it is difficult to realize a significant suppression for higher modes (Landau levels). Notably, in the absence of substantial suppressions to the proton decay rate, the superpartners must be lighter than 100 TeV to satisfy proton decay constraints. We highlight that multiple correlated signals of proton decay could verify this scenario.Comment: 44 pages. v2: References adde

Lectures on Naturalness, String Landscape and Multiverse

The cosmological constant and electroweak hierarchy problem have been a great inspiration for research. Nevertheless, the resolution of these two naturalness problems remains mysterious from the perspective of a low-energy effective field theorist. The string theory landscape and a possible string-based multiverse offer partial answers, but they are also controversial for both technical and conceptual reasons. The present lecture notes, suitable for a one-semester course or for self-study, attempt to provide a technical introduction to these subjects. They are aimed at graduate students and researchers with a solid background in quantum field theory and general relativity who would like to understand the string landscape and its relation to hierarchy problems and naturalness at a reasonably technical level. Necessary basics of string theory are introduced as part of the course. This text will also benefit graduate students who are in the process of studying string theory at a deeper level. In this case, the present notes may serve as additional reading beyond a formal string theory course.Comment: Author version of a book published by Springer, 274 pages LaTeX, 52 figures, v2: errors corrected, references added, v3: further correction

Inducing the mu and the B mu Term by the Radion and the 5d Chern-Simons Term

In 5-dimensional models with gauge-Higgs unification, the F-term vacuum expectation value of the radion provides, in close analogy to the Giudice-Masiero mechanism, a natural source for the mu and B mu term. Both the leading order gauge theory lagrangian and the supersymmetric Chern-Simons term contain couplings to the radion superfield which can be used for this purpose. We analyse the basic features of this mechanism for mu term generation and provide an explicit example, based on a variation of the SU(6) gauge-Higgs unification model of Burdman and Nomura. This construction contains all the relevant features used in our generic analysis. More generally, we expect our mechanism to be relevant to many of the recently discussed orbifold GUT models derived from heterotic string theory. This provides an interesting way of testing high-scale physics via Higgs mass patterns accessible at the LHC.Comment: 23 pages, LaTeX, 1 figure, concrete model significantly improved, references adde

D7-Brane Chaotic Inflation

We analyze string-theoretic large-field inflation in the regime of spontaneously-broken supergravity with conventional moduli stabilization by fluxes and non-perturbative effects. The main ingredient is a shift-symmetric Kahler potential, supplemented by flux-induced shift symmetry breaking in the superpotential. The central technical observation is that all these features are present for D7-brane position moduli in Type IIB orientifolds, allowing for a realization of the axion monodromy proposal in a controlled string theory compactification. On the one hand, in the large complex structure regime the D7-brane position moduli inherit a shift symmetry from their mirror-dual Type IIA Wilson lines. On the other hand, the Type IIB flux superpotential generically breaks this shift symmetry and allows, by appealing to the large flux discretuum, to tune the relevant coefficients to be small. The shift-symmetric direction in D7-brane moduli space can then play the role of the inflaton: While the D7-brane circles a certain trajectory on the Calabi-Yau many times, the corresponding F-term energy density grows only very slowly, thanks to the above-mentioned tuning of the flux. Thus, the large-field inflationary trajectory can be realized in a regime where Kahler, complex structure and other brane moduli are stabilized in a conventional manner, as we demonstrate using the example of the Large Volume Scenario.Comment: 8 pages, 2 figures; v2: references adde

Tuning and Backreaction in F-term Axion Monodromy Inflation

We continue the development of axion monodromy inflation, focussing in particular on the backreaction of complex structure moduli. In our setting, the shift symmetry comes from a partial large complex structure limit of the underlying type IIB orientifold or F-theory fourfold. The coefficient of the inflaton term in the superpotential has to be tuned small to avoid conflict with Kahler moduli stabilisation. To allow such a tuning, this coefficient necessarily depends on further complex structure moduli. At large values of the inflaton field, these moduli are then in danger of backreacting too strongly. To avoid this, further tunings are necessary. In weakly coupled type IIB theory at the orientifold point, implementing these tunings appears to be difficult if not impossible. However, fourfolds or models with mobile D7-branes provide enough structural freedom. We calculate the resulting inflaton potential and study the feasibility of the overall tuning given the limited freedom of the flux landscape. Our preliminary investigations suggest that, even imposing all tuning conditions, the remaining choice of flux vacua can still be large enough for such models to provide a promising path to large-field inflation in string theory.Comment: 46 pages, 6 figures; v2: typos removed, references added; v3: references adde

Towards Axion Monodromy Inflation with Warped KK-Modes

We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. We derive the system of differential equations required to treat this effect quantitatively. Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy.Comment: 28 pages, 3 figures; v2: references added; v3: Corrected an underestimate of supergravity back-reaction in Eq. (36); results changed accordingly; added section 6 which develops the methodology for the 10d non-linear back-reaction; added reference