Abstract
The recent paper arXiv:1205.6881 has developed superform formulations for two versions of the vector-tensor multiplet and their Chern-Simons couplings in fourdimensional \(\mathcal{N}=2\) conformal supergravity. One of them is the standard vector-tensor multiplet with the central charge gauged by a vector multiplet. The other is the variant vector-tensor multiplet with the property that its own one-form gauges the central charge. Here a more general setup is presented in which the known versions reside as special cases. Analysis of the setup demonstrates that under certain assumptions there are two distinct variants, corresponding to the two formulations in arXiv:1205.6881. This provides a classification scheme for vector-tensor multiplets.
We then show that our superspace description leads to an efficient means of deriving component actions in supergravity. The entire action including all fermionic terms is derived for the non-linear vector-tensor multiplet. This extends the results of de Wit et al. in hep-th/9710212, where only the bosonic sector appeared. Finally, the bosonic sector of the action for the variant vector-tensor multiplet is given.
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References
P. Fayet, Fermi-Bose Hypersymmetry, Nucl. Phys. B 113 (1976) 135 [INSPIRE].
M. Sohnius, Supersymmetry and Central Charges, Nucl. Phys. B 138 (1978) 109 [INSPIRE].
M. Sohnius, K. Stelle and P.C. West, Off-mass shell formulation of extended supersymmetric gauge theories, Phys. Lett. B 92 (1980) 123 [INSPIRE].
M. Sohnius, K. Stelle and P.C. West, Dimensional reduction by legendre transformation generates off-shell supersymmetric Yang-Mills theories, Nucl. Phys. B 173 (1980) 127 [INSPIRE].
M.F. Sohnius, K.S. Stelle and P.C. West, Representations of extended supersymmetry, in Superspace and Supergravity, S.W. Hawking and M. Roček eds., Cambridge University Press, Cambridge, U.K. (1981), pg. 283.
B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N = 2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53 [hep-th/9504006] [INSPIRE].
B. Milewski, Superfield formulation of the N = 2 super Yang-Mills model with central charge, Phys. Lett. B 112 (1982) 148 [INSPIRE].
B. Milewski, N = 1 superspace formulation of N = 2 and N = 4 super Yang-Mills models with central charge, Nucl. Phys. B 217 (1983) 172 [INSPIRE].
P. Claus, B. de Wit, M. Faux, B. Kleijn, R. Siebelink and P. Termonia, The Vector-tensor supermultiplet with gauged central charge, Phys. Lett. B 373 (1996) 81 [hep-th/9512143] [INSPIRE].
P. Claus, P. Termonia, B. de Wit and M. Faux, Chern-Simons couplings and inequivalent vector-tensor multiplets, Nucl. Phys. B 491 (1997) 201 [hep-th/9612203] [INSPIRE].
P. Claus, B. de Wit, M. Faux, B. Kleijn, R. Siebelink and P. Termonia, N = 2 supergravity Lagrangians with vector-tensor multiplets, Nucl. Phys. B 512 (1998) 148 [hep-th/9710212] [INSPIRE].
A. Hindawi, B.A. Ovrut and D. Waldram, Vector-tensor multiplet in N = 2 superspace with central charge, Phys. Lett. B 392 (1997) 85 [hep-th/9609016] [INSPIRE].
R. Grimm, M. Hasler and C. Herrmann, The N = 2 vector-tensor multiplet, central charge superspace and Chern-Simons couplings, Int. J. Mod. Phys. A 13 (1998) 1805 [hep-th/9706108] [INSPIRE].
I. Buchbinder, A. Hindawi and B.A. Ovrut, A Two form formulation of the vector-tensor multiplet in central charge superspace, Phys. Lett. B 413 (1997) 79 [hep-th/9706216] [INSPIRE].
N. Dragon, S.M. Kuzenko and U. Theis, The Vector-tensor multiplet in harmonic superspace, Eur. Phys. J. C 4 (1998) 717 [hep-th/9706169] [INSPIRE].
N. Dragon and S.M. Kuzenko, Selfinteracting vector-tensor multiplet, Phys. Lett. B 420 (1998) 64 [hep-th/9709088] [INSPIRE].
E. Ivanov and E. Sokatchev, On nonlinear superfield versions of the vector tensor multiplet, Phys. Lett. B 429 (1998) 35 [hep-th/9711038] [INSPIRE].
N. Dragon, E. Ivanov, S. Kuzenko, E. Sokatchev and U. Theis, N = 2 rigid supersymmetry with gauged central charge, Nucl. Phys. B 538 (1999) 411 [hep-th/9805152] [INSPIRE].
S.M. Kuzenko and J. Novak, Vector-tensor supermultiplets in AdS and supergravity, JHEP 01 (2012) 106 [arXiv:1110.0971] [INSPIRE].
D. Butter and J. Novak, Component reduction in N = 2 supergravity: the vector, tensor and vector-tensor multiplets, JHEP 05 (2012) 115 [arXiv:1201.5431] [INSPIRE].
J. Novak, Superform formulation for vector-tensor multiplets in conformal supergravity, JHEP 09 (2012) 060 [arXiv:1205.6881] [INSPIRE].
L. Andrianopoli, R. D’Auria and L. Sommovigo, D = 4, N = 2 supergravity in the presence of vector-tensor multiplets and the role of higher p-forms in the framework of free differential algebras, Adv. Stud. Theor. Phys. 1 (2008) 561 [arXiv:0710.3107] [INSPIRE].
L. Andrianopoli, R. D’Auria, L. Sommovigo and M. Trigiante, D = 4, N = 2 Gauged Supergravity coupled to Vector-Tensor Multiplets, Nucl. Phys. B 851 (2011) 1 [arXiv:1103.4813] [INSPIRE].
S. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, 4D N = 2 Supergravity and Projective Superspace, JHEP 09 (2008) 051 [arXiv:0805.4683] [INSPIRE].
S. Kuzenko, U. Lindström, M. Roček and G. Tartaglino-Mazzucchelli, On conformal supergravity and projective superspace, JHEP 08 (2009) 023 [arXiv:0905.0063] [INSPIRE].
D. Butter, N = 2 Conformal Superspace in Four Dimensions, JHEP 10 (2011) 030 [arXiv:1103.5914] [INSPIRE].
U. Theis, New N = 2 supersymmetric vector tensor interaction, Phys. Lett. B 486 (2000) 443 [hep-th/0005044] [INSPIRE].
U. Theis, Nonlinear vector tensor multiplets revisited, Nucl. Phys. B 602 (2001) 367 [hep-th/0012096] [INSPIRE].
D. Butter, S.M. Kuzenko and J. Novak, The linear multiplet and ectoplasm, JHEP 09 (2012) 131 [arXiv:1205.6981] [INSPIRE].
P. Breitenlohner and M.F. Sohnius, Superfields, auxiliary fields, and tensor calculus for N = 2 extended supergravity, Nucl. Phys. B 165 (1980) 483[INSPIRE].
B. de Wit, J. van Holten and A. Van Proeyen, Central charges and conformal supergravity, Phys. Lett. B 95 (1980) 51 [INSPIRE].
S.M. Kuzenko and S. Theisen, Correlation functions of conserved currents in N = 2 superconformal theory, Class. Quant. Grav. 17 (2000) 665 [hep-th/9907107] [INSPIRE].
A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge, U.K. (2001).
P.S. Howe, Supergravity in superspace, Nucl. Phys. B 199 (1982) 309 [INSPIRE].
S.J. Gates Jr., Ectoplasm has no topology: the Prelude, hep-th/9709104 [INSPIRE].
S.J. Gates Jr., Ectoplasm has no topology, Nucl. Phys. B 541 (1999) 615 [hep-th/9809056] [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt-Wehlau and W. Siegel, Component actions from curved superspace: normal coordinates and ectoplasm, Phys. Lett. B 421 (1998) 203 [hep-th/9711151] [INSPIRE].
T. Voronov, Geometric integration theory on supermanifolds, Sov. Sci. Rev. C 9 (1992) 1.
M.F. Hasler, The Three form multiplet in N = 2 superspace, Eur. Phys. J. C 1 (1998) 729 [hep-th/9606076] [INSPIRE].
G. Akemann, R. Grimm, M. Hasler and C. Herrmann, N = 2 central charge superspace and a minimal supergravity multiplet, Class. Quant. Grav. 16 (1999) 1617 [hep-th/9812026] [INSPIRE].
R. Grimm, M. Sohnius and J. Wess, Extended Supersymmetry and Gauge Theories, Nucl. Phys. B 133 (1978) 275 [INSPIRE].
B. de Wit, J. van Holten and A. Van Proeyen, Transformation Rules of N = 2 Supergravity Multiplets, Nucl. Phys. B 167 (1980) 186 [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
B. de Wit, J. van Holten and A. Van Proeyen, Structure of N = 2 Supergravity, Nucl. Phys. B 184 (1981) 77 [Erratum ibid. B 222 (1983) 516] [INSPIRE].
B. de Wit, P. Lauwers and A. Van Proeyen, Lagrangians of N = 2 Supergravity - Matter Systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].
B. de Wit, R. Philippe and A. Van Proeyen, The improved tensor multiplet in N = 2 supergravity, Nucl. Phys. B 219 (1983) 143 [INSPIRE].
I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity or a Walk Through Superspace, IOP, Bristol, U.K. (1998).
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ArXiv ePrint: 1210.8325
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Novak, J. Variant vector-tensor multiplets in supergravity: classification and component reduction. J. High Energ. Phys. 2013, 53 (2013). https://doi.org/10.1007/JHEP03(2013)053
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DOI: https://doi.org/10.1007/JHEP03(2013)053