Abstract
The exotic \(\mathcal{N} = (3,1)\) and \(\mathcal{N} = (4,0)\) supergravity theories in six dimensions are theories describing potentials with mixed-symmetry indices satisfying a second order self-duality relation, and giving rise to maximal supergravity in five dimensions upon dimensional reduction. After reviewing how the linearised equations are constructed, we show how introducing additional gauge symmetries one can derive the same equations from first-order self-duality relations. We discuss how this result can be used to obtain a covariant lagrangian.
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Notes
With this we mean fields that produce polarisations of at most spin 2 when dimensionally reduced to four dimensions.
Here and in the following we denote with \(a,b,...\) the fundamental of the first symplectic group and with \(\alpha ,\beta ,...\) the fundamental of the second. Multiple indices are always meant to be antisymmetric.
REFERENCES
J. A. Strathdee, “Extended Poincare supersymmetry,” Int. J. Mod. Phys. A 2, 273 (1987).
C. M. Hull, “Strongly coupled gravity and duality,” Nucl. Phys. B 583, 237 (2000); hep-th/0004195.
C. M. Hull, “Symmetries and compactifications of (4,0) conformal gravity,” J. High Energy Phys. 0012, 007 (2000); hep-th/0011215.
C. M. Hull, “Duality in gravity and higher spin Gauge fields,” J. High Energy Phys. 0109, 027 (2001); hep-th/0107149.
T. Curtright, “Generalized Gauge fields,” Phys. Lett. B 165, 304 (1985). https://doi.org/10.1016/0370-2693(85)91235-3
P. de Medeiros and C. Hull, “Exotic tensor gauge theory and duality,” Commun. Math. Phys. 235, 255 (2003); hep-th/0208155.
M. Henneaux and C. Teitelboim, “Dynamics of chiral (selfdual) P forms,” Phys. Lett. B 206, 650 (1988).
M. Henneaux, V. Lekeu, and A. Leonard, “Chiral tensors of mixed Young symmetry,” Phys. Rev. D 95, 084040 (2017); arXiv: 1612.02772 [hep-th].
M. Henneaux, V. Lekeu, and A. Leonard, “The action of the (free) (4, 0)-theory,” J. High Energy Phys. 1801, 114 (2018);
J. High Energy Phys. 1805, 105(E) (2018); arXiv: 1711.07448 [hep-th].
M. Henneaux, V. Lekeu, J. Matulich, and S. Prohazka, “The action of the (free)\(\mathcal{N}\) = (3,1) theory in six spacetime dimensions,” J. High Energy Phys. 1806, 057 (2018); arXiv: 1804.10125 [hep-th].
P. Pasti, D. P. Sorokin, and M. Tonin, “On Lorentz invariant actions for chiral p forms,” Phys. Rev. D 55, 6292 (1997); hep-th/9611100.
Y. M. Zinoviev, “First order formalism for mixed symmetry tensor fields,” hep-th/0304067.
L. Borsten, “D = 6, \(\mathcal{N}\) = (2,0) and 𝒩 = (4,0) theories,” Phys. Rev. D 97, 066014 (2018); arXiv: 1708.02573 [hep-th].
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Galati, G., Riccioni, F. On Exotic Six-Dimensional Supergravity Theories. Phys. Part. Nuclei Lett. 17, 650–653 (2020). https://doi.org/10.1134/S1547477120050155
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DOI: https://doi.org/10.1134/S1547477120050155