Conifold dynamics and axion monodromies

Published for SISSA by Springer Received: August 11, 2020 Accepted: September 21, 2020 Published: October 21, 2020 M. Scalisi, P. Soler, V. Van Hemelryck and T. Van Riet Institute of Theoretical Physics, KU Leuven, Celestijnenlaan 200D B-3001 Leuven, Belgium E-mail: , , , Abstract: It has recently been appreciated that the conifold modulus plays an important role in string-phenomenological set-ups involving warped throats, both by imposing constraints on model building and for obtaining a 10-dimensional picture of SUSY-breaking. In this note, we point out that the stability of the conifold modulus furthermore prevents large super-Planckian axion monodromy field ranges caused by brane-flux decay processes down warped throats. Our findings imply a significant challenge for concrete string theory embeddings of the inflationary flux-unwinding scenario. Keywords: D-branes, Flux compactifications, Superstring Vacua ArXiv ePrint: 2007.15391 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP10(2020)133 JHEP10(2020)133 Conifold dynamics and axion monodromies Contents 1 2 The conifold and brane-flux moduli 2.1 The conifold modulus 2.2 SUSY breaking and the conifold instability 2.3 The brane-flux transition modulus 3 3 5 6 3 Uplifting 5-brane runaway 7 4 Axion monodromies and field range bounds 4.1 General considerations 4.2 Anti-brane annihilation 4.3 Brane creation from fluxes 9 9 11 15 5 Discussion 16 A Mass ratio of the conifold and brane-flux moduli 16 1 Introduction Warped throats provide some of the most interesting playgrounds for string phenomenology due to their capacity of generating exponential hierarchies between energy scales. One of their most remarkable roles arises in the context of supersymmetry (SUSY) breaking and, in particular, in the construction of de Sitter (dS) vacua [1]. Long throats can be used to suppress and keep control over SUSY breaking effects induced by anti-D3-branes to an otherwise SUSY geometry. Anti-branes naturally live at the tip of warped throats and see their tensions exponentially redshifted. Under the right circumstances, this tension may provide just enough energy to generate a net positive vacuum energy, yet be small enough to maintain perturbative control and to not destabilise the geometry. Despite thorough scrutiny, the viability of dS uplifts in concrete compactifications and the required delicate balance of hierarchies is still the subject of much debate (see [2] and [3] for recent discussions from complementary viewpoints). The existing controversy regarding the dS landscape in string theory has only been rising since it became part of the web of Swampland conjectures that de Sitter vacua might simply not be there at all [2, 4, 5] (see [6–10] for related ideas) or have dramatic shorter lifespans than assumed sofar [11].1 Part of the recent efforts have been devoted to analysing the effects that light geometric modes localised down warped throats can have on the effective theory. For instance, local 1 The idea of the Swampland was first contemplated in [12] and reviewed recently in [13]. –1– JHEP10(2020)133 1 Introduction –2– JHEP10(2020)133 KK modes cannot really be decoupled from the 4d effective field theory (EFT) although their couplings might be rather harmless and they could just behave as spectators [14]. Of particular importance is the so-called conifold modulus, which is the local complex structure modulus of the throat first studied by Douglas and collaborators in [15]. This field has a mass scale that is not as light as the Kähler moduli but is much lighter than the complex structure moduli of the bulk Calabi-Yau (CY). It has been recently appreciated that it might affect the stability of the KKLT scenario if flux numbers are too low [14, 16–18]. At the same time, it is claimed to be crucial for reaching a detailed 10d understanding of how anti-brane uplifting could work [19]. Moduli stabilisation scenarios with long warped throats are not only useful in the study of dS vacua. As pointed out in [20, 21], such set-ups can incorporate models of axion monodromy with large (in principle transplanckian) field ranges (see also [22–25] These have potential implications for phenomenology, in particular for the construction of models of large field inflation. More importantly, they represents an explicit framework where conceptual issues associated to transplanckian field displacements can be analysed in detail. The Swampland distance conjecture (SDC) [26] provides in fact a concrete argument why EFTs compatible with quantum gravity should not allow for parametrically large field displacements ∆φ  MPl within their regime of validity. The typical obstruction would come from an infinite tower of states becoming exponentially light along a trajectory in field space, which leads to a decrease of the quantum gravity cut-off [27, 28]. Detailed investigations in string theory have in fact verified this statement repeatdly [29–38], while others have failed to find fully trustworthy models where field ranges can extend parametrically beyond the Planck range. Models of axion monodromy are arguably the set-ups where the Swampland distance conjecture constraints are most challenging to understand and are still the subject of debate [39–44]. In this note, we focus on the axion monodromy scenario of [20, 21] in order to concretely examine the obstructions arising in warped throats when one tries to engineer super-Planckian excursions. We will in fact argue that the conifold modulus plays a crucial role in preventing parametrically large field displacement, when supersymmetry is broken, within the EFT. Our analysis is similar in several aspects to the one of [14, 16–18] but incorporates the interplay of the conifold modulus with the axion-like field parametrising the process of brane-flux annihilation of [45]. We find that a large number of monodromies, and hence a large field displacement, cannot be achieved without destabilising the geometry along the direction parametrised by the conifold modulus. Our analysis is independent of the mechanism of volume stabilisation, and is hence applicable to diverse scenarios such as KKLT [1] or the large volume scenario [46]. While some particular set-ups may provide other means by which transplanckian distances are censored, the conifold destabilisation mechanism we study is universal. The rest of this note is organised as follows. In section 2 we introduce two fields that play a crucial role in our analysis; the conifold modulus S and an open-string modulus ψ that mediates brane-flux transitions, which will be our axion-like scalar that undergoes monodromies. Since the brane-flux decay process inside compact CYs is crucial for our analysis we treat this separately in section 3. Here we discuss both the decay of NSNS and RR flux, and whether the stability of the conifold modulus leads to stronger constraints on meta-stable dS uplifts (...truncated)