New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!

TL;DR

The work constructs an extended set of $N=2$ locally supersymmetric higher-derivative invariants from full superspace integrals, allowing unrestricted chiral multiplets, vector multiplets, and the Weyl multiplet, with off-shell supersymmetry. A key tool is the kinetic multiplet $\mathbb{T}(\bar{\Phi})$, generating $F^4$, $R^2F^2$, and $R^4$ couplings that can be organized through a real Kähler-like potential $\mathcal{H}(X,\bar{X})$, yielding a Kähler-covariant action. The authors prove a non-renormalization theorem showing that these invariants do not contribute to the entropy or electric charges of BPS black holes, providing a potential explanation for the observed agreement between microstate counting and supergravity at subleading order. They also discuss connections to topological string deformations and outline pathways to richer hierarchies via nested and multiple kinetic multiplets, suggesting an infinite landscape of higher-derivative supersymmetric couplings. Overall, the paper lays groundwork for systematic inclusion of full-superspace higher-derivative terms in $N=2$ supergravity and clarifies their (limited) impact on BPS black hole physics.

Abstract

An extended class of N=2 locally supersymmetric invariants with higher-derivative couplings based on full superspace integrals, is constructed. These invariants may depend on unrestricted chiral supermultiplets, on vector supermultiplets and on the Weyl supermultiplet. Supersymmetry is realized off-shell. A non-renormalization theorem is proven according to which none of these invariants can contribute to the entropy and electric charges of BPS black holes. Some of these invariants may be relevant for topological string deformations.