Off-shell N=2 tensor supermultiplets

TL;DR

The paper develops an off-shell framework for $N=2$ tensor supermultiplets with an arbitrary count $n$, unifying rigid, superconformal, and Poincaré supergravity couplings. It constructs composite reduced chiral multiplets from tensor multiplets via a real SU(2)-invariant potential, encodes Lagrangians in terms of a prepotential $F_{IJ}$, and shows how to dualize tensors to hypermultiplets yielding hyperkähler or quaternion-Kähler targets with abelian isometries. A key ingredient is the superconformal quotient, which yields cone-structured target spaces for tensor, vector, and hypermultiplets and links tensor and hypermultiplet moduli through a Legendre transform. The authors also formulate an off-shell c-map between tensor and vector multiplets and present higher-derivative tensor actions, with the two-tensor case offering an elegant CP-metric classification of self-dual Einstein spaces with two commuting isometries. Together, these results provide a versatile toolkit for constructing and analyzing a broad class of off-shell supergravity theories with tensor multiplets and their higher-derivative generalizations.

Abstract

A multiplet calculus is presented for an arbitrary number n of N=2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkahler or quaternion-Kahler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kahler manifolds with two commuting isometries is given.