The 0-brane action in a general D=4 supergravity background

TL;DR

This work derives a κ-symmetric 0-brane action for a superparticle moving in general D=4 supergravity backgrounds, first in N=2 with vector multiplets and then in N=8, with the scalar couplings governed by the central charge Z. The key result is that the worldline action uses a real coupling R = -2|Z| to yield κ-invariance, and the action corresponds to the black hole source term with mass set by the central charge, consistent with BPS conditions. The authors also show a geometric origin by wrapping a D3-brane on a supersymmetric Calabi–Yau 3-cycle, reproducing the 0-brane action via kinetic and WZ term reductions tied to CY period integrals. In the N=8 extension, they classify 1/2, 1/4, and 1/8 BPS black holes, formulate SU(8)-covariant κ-projections, and construct corresponding 0-brane actions, providing a framework to study 1D superconformal quantum mechanics on AdS2 boundaries and CY moduli dynamics.

Abstract

We begin by presenting the superparticle action in the background of N=2, D=4 supergravity coupled to n vector multiplets interacting via an arbitrary special Kahler geometry. Our construction is based on implementing kappa-supersymmetry. In particular, our result can be interpreted as the source term for N=2 BPS black holes with a finite horizon area. When the vector multiplets can be associated to the complex structure moduli of a Calabi-Yau manifold, then our 0-brane action can be derived by wrapping 3-branes around 3-cycles of the 3-fold. Our result can be extended to the case of higher supersymmetry; we explicitly construct the kappa supersymmetric action for a superparticle moving in an arbitrary N=8 supergravity background with 1/2, 1/4 or 1/8 residual supersymmetry.