The off-shell c-map
Nabamita Banerjee, Bernard de Wit, Stefanos Katmadas

TL;DR
This paper develops an off-shell formulation of the c-map in supergravity, clarifying its structure, extending it to higher-derivative theories, and enabling systematic analysis of complex models.
Contribution
It presents the first off-shell version of the c-map, clarifies its properties, and demonstrates its applicability to higher-derivative supergravity theories.
Findings
Off-shell c-map clarifies intricate issues in supergravity.
Not all tensor multiplet Lagrangians are in the c-map image.
Higher-derivative couplings can be systematically analyzed.
Abstract
The off-shell version of the c-map is presented, based on a systematic off-shell reduction from four to three space-time dimensions for supergravity theories with eight supercharges. In the reduction, the R-symmetry group is enhanced to local [SU(2) x SU(2)]/Z2 =SO(4) and the c-map is effected by a parity transformation in the internal space that interchanges the two SU(2) factors. Vector and tensor supermultiplets are each others conjugate under the c-map and both can be dualized in three dimensions to (on-shell) hypermultiplets. As shown in this paper the off-shell formulation indeed leads to a clarification of many of the intricate issues that play a role in the c-map. The results for off-shell Lagrangians quadratic in space-time derivatives are analyzed in detail and compared to the literature. The underlying reasons are identified why not all of the four-dimensional tensor…
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