On the Possibility of Large Axion Moduli Spaces

We study the diameters of axion moduli spaces, focusing primarily on type IIB compactifications on Calabi-Yau three-folds. In this case, we derive a stringent bound on the diameter in the large volume region of parameter space for Calabi-Yaus with simplicial K\"ahler cone. This bound can be violated by Calabi-Yaus with non-simplicial K\"ahler cones, but additional contributions are introduced to the effective action which can restrict the field range accessible to the axions. We perform a statistical analysis of simulated moduli spaces, finding in all cases that these additional contributions restrict the diameter so that these moduli spaces are no more likely to yield successful inflation than those with simplicial K\"ahler cone or with far fewer axions. Further heuristic arguments for axions in other corners of the duality web suggest that the difficulty observed in hep-th/0303252 of finding an axion decay constant parametrically larger than $M_p$ applies not only to individual axions, but to the diagonals of axion moduli space as well. This observation is shown to follow from the weak gravity conjecture of hep-th/0601001, so it likely applies not only to axions in string theory, but also to axions in any consistent theory of quantum gravity.Comment: 26+11 pages, 9 figures, discussion of relationship to weak gravity conjecture added v2, references added v3, minor changes v4, matches publication versio

Evidence for C-theorems in 6D SCFTs

Using the recently established classification of 6D SCFTs we present evidence for the existence of families of weak C-functions, that is, quantities which decrease in a flow from the UV to the IR. Introducing a background R-symmetry field strength R and a non-trivial tangent bundle T on the 6D spacetime, we consider C-functions given by the linear combinations C = m1 alpha + m2 beta + m3 gamma, where alpha, beta and gamma are the anomaly polynomial coefficients for the formal characteristic classes c2(R)^2, c2(R)p1(T) and p1(T)^2. By performing a detailed sweep over many theories, we determine the shape of the unbounded monotonic region in "m-space" compatible with both Higgs branch flows and tensor branch flows. We also verify that --as expected-- the Euler density conformal anomaly falls in the admissible region.Comment: v2: 25 pages, 9 figures, typos correcte

Persistence of the pattern in the interior of 5d moduli spaces

Castellano, Ruiz, and Valenzuela recently observed a remarkable “pattern” in infinite-distance limits of moduli spaces in quantum gravity, which relates the field space variation of the mass of the lightest tower of particles to the field space variation of the species scale. In this work, we show how a version of this pattern can be proven to hold for BPS particles and strings throughout the vector multiplet moduli space of a 5d supergravity theory, even in regions where the particle masses and string tensions are substantially modified relative to their asymptotic behavior in the infinite-distance limits. This suggests that a suitably defined version of the pattern may hold not merely in the asymptotic limits of moduli space, but in the interior as well

Evidence for a Lattice Weak Gravity Conjecture

The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at every lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling $e$ exists, then the fundamental gravitational cutoff energy of the theory is no higher than $\sim e^{1/3} M_{\rm Pl}$.Comment: v2: 41 pages, typos fixed, references added, substantial revisions and clarifications (conclusions unchanged