Axion decay constants at special points in type II string theory

Published for SISSA by Springer Received: October 5, 2016 Accepted: December 26, 2016 Published: January 16, 2017 Masaki Honda, Akane Oikawa and Hajime Otsuka Department of Physics, Waseda University, Tokyo 169-8555, Japan E-mail: yakkuru , , Abstract: We propose the mechanism to disentangle the decay constant of closed string axion from the string scale in the framework of type II string theory on Calabi-Yau manifold. We find that the quantum and geometrical corrections in the prepotential that arise at some special points in the moduli space widen the window of axion decay constant. In particular, around the small complex structure points, the axion decay constant becomes significantly lower than the string scale. We also discuss the moduli stabilization leading to the phenomenologically attractive low-scale axion decay constant. Keywords: Strings and branes phenomenology ArXiv ePrint: 1608.08372 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP01(2017)064 JHEP01(2017)064 Axion decay constants at special points in type II string theory Contents 1 2 Decay constant of closed string axion 3 3 Axion decay constant around the special point 3.1 SCS point 3.1.1 α1 6= α2 6= α3 6= α4 3.1.2 α1 6= α2 6= α3 = α4 3.1.3 α1 = α2 6= α3 = α4 3.1.4 α1 = α2 = α3 = α4 3.2 Conifold point 3.3 LCS point 3.3.1 Single axion 3.3.2 Multiple axions 6 6 9 10 13 14 15 17 19 20 4 Massless axion and moduli stabilization 22 5 Conclusion 25 1 Introduction An axion, or axion-like particle, is phenomenologically and cosmologically attractive particle to explain the origin of tiny strong CP phase in the standard model [1], the current dark matter abundance [2–4] and the origin of cosmological microwave background through the inflation mechanism. The consistent theory of quantum gravity such as the string theory also predicts the existence of axion particles through the dimensional reduction of the higher-dimensional vector and tensor fields associated with the internal cycles of extradimensional space. In particular, the QCD axion decay constant should be within the range, 10 9−12 GeV by the observation of supernova (SN) 1987A [5, 6] and dark matter abundance observed by Planck [7] with O(1) initial misalignment angle.(For a review, see, e.g., ref. [8].) From the inflationary point of view, the decay constant of axion inflaton is severely constrained by the Planck data [7], e.g., 1018−19 GeV for the natural inflation [9]. It is difficult to extract the above constrained axion decay constant from the string theory. The authors of refs. [10–12] showed that decay constant of closed string axion in the string theory is typically around 1016−17 GeV, since both the decay constant and the gauge coupling of visible sector are closely related through the volume of extra-dimensional space. When the visible sector lives on the localized cycle of extra-dimensional space, the decay constant of axion associated –1– JHEP01(2017)064 1 Introduction 1 The warped string compactification is also discussed in ref. [15]. See for other axions irrelevant with the internal cycle of extra-dimensional space in heterotic string [16] and type IIA string [17]. –2– JHEP01(2017)064 with the large volume cycle can be taken much smaller than Planck scale [13], which is achieved in so-called LARGE Volume Scenario (LVS) in type IIB string theory [14].1 On the other hand, the larger axion decay constant is obtained by the inclusion of the quantum corrections to the volume of extra-dimensional space [18], one-loop corrections for the gauge couplings [19, 20], and the alignment mechanism in terms of multiple axions [21]. In this paper, we focus on Kähler (complex structure) moduli fields in type IIA (IIB) string theory on Calabi-Yau (CY) manifold. These moduli potentials receive the quantum (geometrical) corrections which are exactly calculated in the topological string theory. Recently, the authors of ref. [18] have showed that the axion decay constant including the instanton corrections has the maximum value in type IIA string on CY manifold with a few moduli fields around the large volume limit, which corresponds to the large complex structure (LCS) limit in type IIB string on mirror CY manifold. In this case, even if the volume of internal cycle is of O(1) in string units, such instanton corrections give the sizable effect. In this way, it motivates us to proceed to study the detail of the quantum and geometrical corrections for a decay constant of closed string axion around the several points of moduli spaces. In type IIB string theory on CY manifold, these geometrical and non-perturbative corrections are exactly obtained by solving the corresponding PicardFuchs differential equation for the period vector of CY manifold, which corresponds to the instanton corrections in type IIA side. We in particular focus on the regular singular points involved in the Picard-Fuchs equation which are called as the special points of moduli space, such as the LCS point, conifold point, and small complex structure (SCS) point involving the Gepner point [22, 23]. These closed string axions then naturally appear around the special points in the low-energy effective theory, since the monodromy symmetries around special points allow the existence of axions in the moduli Kähler potential. Around these special points, we proceed to study the detail of the quantum and geometrical corrections for a decay constant of closed string axion. It is remarkable that in type IIB string theory, the decay constants of axions associated with the complex structure moduli are irrelevant to the volume of mirror CY manifold, i.e., the string scale, in comparison with those of Kähler moduli. As pointed out in refs. [24–26], it is interesting to discuss the phenomenology and cosmology of complex structure moduli. The remaining of this paper is organized as follows. After briefly reviewing the Kähler potential on the basis of N = 2 special geometry in section 2, we first show how to define the axion particles around the special points of complex structure moduli space and corresponding decay constant. The axionic shift symmetries are then captured by the invariance of Kähler potential under the monodromy transformation at the special points. In section 3.1, we formulate the geometrical corrections for the period vector of CY manifold with an emphasis on the SCS point. It is then found that, in contrast to the previous studies, the decay constant of closed string axion associated with the complex structure modulus is taken much smaller than the string scale, and such a property is a common phenomena in typical one-parameter CY manifolds. Next, we proceed to estimate the axion decay constant around the conifold point in section 3.2 and LCS point in section 3.3. Finally, we comment on the moduli stabilization to generate the low-scale axion decay constants in section 4. Section 5 is devoted to the conclusion. 2 Decay const (...truncated)