Superradiance in String Theory

Abstract

We perform an extensive analysis of the statistics of axion masses and interactions in compactifications of type IIB string theory, and we show that black hole superradiance excludes some regions of Calabi-Yau moduli space. Regardless of the cosmological model, a theory with an axion whose mass falls in a superradiant band can be probed by the measured properties of astrophysical black holes, unless the axion selfinteraction is large enough to disrupt formation of a condensate. We study a large ensemble of compactifications on Calabi-Yau hypersurfaces, with 1 ≤ h 1,1 ≤ 491 closed string axions, and determine whether the superradiance conditions on the masses and self-interactions are fulfilled. The axion mass spectrum is largely determined by the Kähler parameters, for mild assumptions about the contributing instantons, and takes a nearly-universal form when h 1,11. When the Kähler moduli are taken at the tip of the stretched Kähler cone, the fraction of geometries excluded initially grows with h 1,1 , to a maximum of ≈ 0.5 at h 1,1 ≈ 160, and then falls for larger h 1,1 . Further inside the Kähler cone, the superradiance constraints are far weaker, but for h 1,1 100 the decay constants are so small that these geometries may be in tension with astrophysical bounds, depending on the realization of the Standard Model.

Moduli Stabilisation and the Statistics of Axion Physics in the Landscape

“…They hold at fixed h 1,1 when moving in the Kähler moduli space by varying microscopic parameters like g s after the decay constants are written in terms of them thanks to moduli stabilisation. These results are complementary to the ones of [27,28] (see also [29] for qualitatively similar findings) which found an approximate log-normal distribution for the axion decay constants of a given CY model focusing at the tip of the stretched Kähler cone. Moreover they found that the mean value of the f θ i 's decreases when h 1,1 increases.…”

“…Interestingly, they found that the mean value of f a decreases as h 1,1 increases. Our results are complementary to the ones of [27,28] since we included moduli stabilisation and worked out the distribution of f a and m a as a function of flux quanta, i.e. moving in the moduli space at fixed h 1,1 .…”

“…Moreover they found that the mean value of the f θ i 's decreases when h 1,1 increases. Given that the tip of the stretched Kähler cone corresponds to the smallest values of the Kähler moduli which are compatible with a controlled α expansion, and the axion decay constants are inversely proportional to 4-cycle volumes, the values of the f θ i 's obtained by [27,28] represent the largest values of the axion decay constants compatible with a trustable EFT. These values would therefore provide an upper bound for the regime of validity of our logarithmic distributions (3.8) which can be integrated with the results of [27,28] to describe how the number of flux vacua changes has a function of both f θ i and h 1,1 .…”

“…Moreover, ref. [27,28] derived the distributions of the axion decay constants and masses for different values of h 1,1 but at a given point in the moduli space, focusing in particular on the tip of the so-called stretched Kähler cone, i.e. the point closest to the origin which allows to keep the EFT under control.…”

“…moving in the moduli space at fixed h 1,1 . The results of [27,28] can be integrated with ours since they provide the boundaries of the region in moduli space where the EFT is under control and our logarithmic distributions can be trusted, i.e. our logarithmic distributions are valid for f a f a,max (h 1,1 ) or m a m a,max (h 1,1 ) with f a,max (h 1,1 ) and m a,max (h 1,1 ) as given in [27,28] as a function of the number of Kähler moduli h 1,1 .…”