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 \( \left[\mathrm{S}\mathrm{U}(2)\times \mathrm{S}\mathrm{U}(2)\right]/{\mathbb{Z}}_2=\mathrm{SO}(4) \) 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 multiplet Lagrangians can be in the image of the c-map. The advantage of the off-shell approach is, that it also enables a systematic analysis of theories with higher-derivative couplings. This is demonstrated for a particular subclass of such theories, which, under certain conditions, are consistent under the c-map. In principle, explicit results for realistic four-dimensional type-II string compactifications can be explored in this way.
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ArXiv ePrint: 1512.06686
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Banerjee, N., de Wit, B. & Katmadas, S. The off-shell c-map. J. High Energ. Phys. 2016, 156 (2016). https://doi.org/10.1007/JHEP01(2016)156
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DOI: https://doi.org/10.1007/JHEP01(2016)156