Superconformal Sigma Models

(Super)conformal mechanics are believed to describe the radial motion of (super)particles in the near-horizon AdS geometry of (supersymmetric)black holes. One-dimensional conformal sigma models have been extensively studied for various numbers of supersymmetries. In this work, we investigate one-dimensional gauged superconformal sigma models that admit the exceptional one-parameter supergroup D(2,1; α) as their symmetry group; the most general N = 4 superconformal group in one dimension. We determine the structural and geometric conditions required for Lagrangian invariance and the closure of the superconformal algebra.

Our analysis reveals classes of one-dimensional sigma models that are only scale-invariant before gauging but become fully conformally invariant after gauging a specific isometry group. Among these, the N = 4B cases are particularly notable, as they contain a physically relevant subclass. Specifically, for α = 0, the model effectively describes an n-node Coulomb branch quiver quantum mechanics. This D(2,1; 0)-invariant gauged sigma model corresponds to a supergravity counterpart describing dyonic BPS black holes in an asymptotic AdS₂ × S² spacetime.