Thraxions: ultralight throat axions

Published for SISSA by Springer Received: January 18, 2019 Revised: March 26, 2019 Accepted: April 18, 2019 Published: April 29, 2019 Thraxions: ultralight throat axions a Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany b Deutsches Elektronen-Synchrotron, DESY, Notkestraße 85, 22607 Hamburg, Germany E-mail: , , , Abstract: We argue that a new type of extremely light axion is generically present in the type IIB part of the string theory landscape. Its mass is suppressed by the third power of the warp factor of a strongly warped region (Klebanov-Strassler throat), suggesting the name thraxion. Our observation is based on the generic presence of several throats sharing the same 2-cycle. This cycle shrinks to zero volume at the end of each throat. It is hence trivial in homology and the corresponding C2 axion is massive. However, the mass is warpingsuppressed since, if one were to cut off the strongly warped regions, a proper 2-cycle would re-emerge. Since the kinetic term of the axion is dominated in the UV, an even stronger, quadratic mass suppression results. Moreover, if the axion is excited, the angular modes of the throats backreact. This gives our effective C2 axion a finite monodromy and flattens its potential even further. Eventually, the mass turns out to scale as the third power of the warp factor. We briefly discuss possible implications for phenomenology and potential violations of the Weak Gravity Conjecture for axions. Moreover we identify a mechanism for generating super-Planckian axionic field ranges which we call drifting monodromies. However, in the examples we consider, the potential oscillates on sub-Planckian distances in field space, preventing us from building a natural inflation model on the basis of this idea. Keywords: Strings and branes phenomenology ArXiv ePrint: 1812.03999 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP04(2019)158 JHEP04(2019)158 Arthur Hebecker,a Sascha Leonhardt,a Jakob Moritzb and Alexander Westphalb Contents 2 2 Backreacted potential of the thraxion from 10d 2.1 Geometric and flux-background 2.1.1 Geometric features of generic CYs 2.1.2 Moduli stabilization by fluxes 2.2 Local backreaction in the throat 2.3 The CY breaking potential 2.4 Discussion of results 2.5 The B2 -axio 4 4 4 6 8 9 11 13 3 Four-dimensional SUGRA completion 3.1 Counting moduli through the conifold transition 3.2 The thraxion superpotential 3.2.1 The GVW superpotential of a multi conifold system 3.2.2 The thraxion as a stabilizer field 3.2.3 The double throat: n = 2, m = 1 3.2.4 The general multi throat 3.3 Comments on the b-Axion 14 15 16 16 17 19 21 22 4 The axion potential and the gauge/gravity correspondence 23 5 Applications 5.1 Thraxions on the quintic: drifting monodromy 5.2 A clash with the weak gravity conjecture 5.3 The spectrum of effective instantons 5.4 Axion phenomenology 5.5 Uplifting 24 24 26 28 29 29 6 Conclusion and discussion 31 A Deformed conifold for general complex structure modulus 33 B The axion potential in the local throat 36 C Derivation and solution of the 5d equations of motion C.1 The 5d action for ϕ C.2 Schrödinger equations and exact solutions for free fields 37 37 39 D Axion decay constant and potential parameters 41 E Background on multi conifolds 43 –1– JHEP04(2019)158 1 Introduction 1 Introduction 1 Note that despite the fact that strongly warped throats are needed to generate a small scalar potential for the axion, the decay constant is not suppressed by warping effects. This is because its internal fieldprofile is not localized at the bottom of the throats, in contrast to some examples that have appeared in the literature [36, 37]. –2– JHEP04(2019)158 Axion-like particles (axions for short) have become a main player in beyond-the-standardmodel (BSM) physics in general [1, 2] and in string phenomenology in particular [3–7]. They are relevant e.g. in the context of the strong CP problem, inflation and as dark matter candidates. Furthermore, in the recent debate surrounding the Landscape/Swampland program [8, 9] and the Weak Gravity Conjecture (WGC) [10], axions have occupied a prominent place [11–19]. This is also related to the question whether or with which parameters axion monodromy [20, 21] can be realized in consistent quantum gravity settings [22–27]. In this paper, we present a novel type of ultralight axion which, as we argue, is generically present in the type IIB part of the landscape, building on a proposal made in [28]. Its extreme lightness, both in absolute terms and in relation to its decay constant (i.e. compared to the scale MP4 exp(−MP /f ) of generic non-perturbative potentials) lets it stand out among the many other stringy axions. It is surprising that, to the best of our knowledge, this very generic axionic degree of freedom was missed at the time when the string axiverse was being intensely studied. Before turning to the details, we want to explain our central and, in our opinion, rather surprising, parametric results: consider type IIB Calabi-Yau orientifold or F-theory models stabilized by fluxes and non-perturbative effects [29–31]. It is generally accepted that Klebanov-Strassler (KS) throats [32] with warp factor wIR  1 will be present in an order-one fraction of such models [33–35]. This warp factor can easily be exponentially small, such that it is justified to focus for the moment only on the dependence on wIR . −1 In other words, let us for now set RCY ∼ Mstring and Nflux ∼ O(1), thus ignoring all parameters except for the warp factor. Naively, the lightest states are then the glueballs (or warped-throat KK modes) with mass ∼ wIR (in Planck units). By contrast, we claim 3 is frequently present in such settings. To be more that an ultralight axion with mass ∼ wIR precise, this happens at least in all cases where the fluxes stabilize the complex structure moduli near a conifold transition point in moduli space. Moreover, our axion has a decay constant f ∼ O(1) in the simplest models,1 which can be enhanced by products of flux numbers to super-Planckian values in more general settings, and an effective potential which can be much smaller than the naive expectation V ∼ exp(−1/f ) cos(φ/f ) (again in Planck units). Clearly, this has potentially many interesting applications, from the WGC for axions to inflation and uplifting. The paper is organized as follows. We start with the background solution in section 2.1. We consider a Calabi-Yau with a conifold point in complex structure moduli space at which multiple three-cycles degenerate simultaneously. We explain why this is a generic feature of Calabi-Yaus. Concentrating on the case of two degenerate three-cycles, we introduce separate deformation parameters zi with phases ϕi = arg zi , i = 1, 2, for the two deformed conifold regions. Crucially, the two conifolds, specifically the S 3 -cycles describing t (...truncated)