We use the superspace formulation of supergravity in eleven and ten dimensions to compute fermion couplings on the M2-brane and on D$p$-branes. In this formulation fermionic couplings arise naturally from the $theta$-expansion of the superfields from
which the brane actions are constructed. The techniques we use and develop can in principle be applied to determine the fermionic couplings to general background fields up to arbitrary order. Starting with the superspace formulation of 11-dimensional supergravity, we use a geometric technique known as the `normal coordinate method to obtain the $theta$-expansion of the M2-brane action. We then present a method which allows us to translate the knowledge of fermionic couplings on the M2-brane to knowledge of such couplings on the D2-brane, and then to any D$p$-brane. This method is based on superspace generalizations of both the compactification taking 11-dimensional supergravity to type IIA supergravity and the T-duality rules connecting the type IIA and type IIB supergravities.
In this note we outline the arguments against the ten-dimensional consistency of the simplest types of KKLT de Sitter vacua, as given in arXiv:1707.08678. We comment on parametrization proposals within four-dimensional supergravity and express our di
sagreement with the recent criticism by the authors of arXiv:1808.09428.
A second order pole in the scalar kinetic term can lead to a class of inflation models with universal predictions referred to as pole inflation or $alpha$-attractors. While this kinetic structure is ubiquitous in supergravity effective field theories
, realising a consistent UV complete model in e.g. string theory is a non-trivial task. For one, one expects quantum corrections arising in the vicinity of the pole which may spoil the typical attractor dynamics. As a conservative estimate of the range of validity of supergravity models of pole inflation we employ the weak gravity conjecture (WGC). We find that this constrains the accessible part of the inflationary plateau by limiting the decay constant of the axion partner. For the original single complex field models, the WGC does not even allow the inflaton to reach the inflationary plateau region. We analyze if evoking the assistance of $N$ scalar fields from the open string moduli helps addressing these problems. Pole $N$-flation could improve radiative control by reducing the required range of each individual field. However, the WGC bound prohibiting pole inflation for a single such field persists even for a collective motion of $N$ such scalars if we impose the sublattice WGC. Finally, we outline steps towards an embedding of pole N-flation in type IIB string theory on fibred Calabi-Yau manifolds.
