Abstract
We provide \( \mathcal{N}=1 \) superfield description of BPS backgrounds in six-dimensional supergravity (6D SUGRA) with 3-branes, which is compactified on a two-dimensional space. The brane terms induce the localized fluxes. We find a useful gauge in which the background equations become significantly simple. This is not the Wess-Zumino gauge, and the relation to the usual component-field expression of 6D SUGRA is not straightforward. One of the equations reduces to the Liouville equation. By moving to the Wess-Zumino gauge, we check that our expressions reproduce the known results of the previous works, which are expressed in the component fields. Our results help us develop the systematic derivation of four-dimensional effective theories that keeps the \( \mathcal{N}=1 \) SUSY structure.
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References
N. Marcus, A. Sagnotti and W. Siegel, Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields, Nucl. Phys. B 224 (1983) 159 [INSPIRE].
N. Arkani-Hamed, T. Gregoire and J.G. Wacker, Higher dimensional supersymmetry in 4D superspace, JHEP 03 (2002) 055 [hep-th/0101233] [INSPIRE].
D. Marti and A. Pomarol, Supersymmetric theories with compact extra dimensions in N = 1 superfields, Phys. Rev. D 64 (2001) 105025 [hep-th/0106256] [INSPIRE].
A. Hebecker, 5D super Yang-Mills theory in 4D superspace, superfield brane operators and applications to orbifold GUTs, Nucl. Phys. B 632 (2002) 101 [hep-ph/0112230] [INSPIRE].
H. Abe, T. Kobayashi, H. Ohki and K. Sumita, Superfield description of 10D SYM theory with magnetized extra dimensions, Nucl. Phys. B 863 (2012) 1 [arXiv:1204.5327] [INSPIRE].
H. Abe, T. Horie and K. Sumita, Superfield description of (4 + 2n)-dimensional SYM theories and their mixtures on magnetized tori, Nucl. Phys. B 900 (2015) 331 [arXiv:1507.02425] [INSPIRE].
W.D. Linch, III, M.A. Luty and J. Phillips, Five-dimensional supergravity in N = 1 superspace, Phys. Rev. D 68 (2003) 025008 [hep-th/0209060] [INSPIRE].
F. Paccetti Correia, M.G. Schmidt and Z. Tavartkiladze, Superfield approach to 5D conformal SUGRA and the radion, Nucl. Phys. B 709 (2005) 141 [hep-th/0408138] [INSPIRE].
H. Abe and Y. Sakamura, Superfield description of 5D supergravity on general warped geometry, JHEP 10 (2004) 013 [hep-th/0408224] [INSPIRE].
E. Bergshoeff, E. Sezgin and A. Van Proeyen, Superconformal tensor calculus and matter couplings in six-dimensions, Nucl. Phys. B 264 (1986) 653 [Erratum ibid. B 598 (2001) 667] [INSPIRE].
F. Coomans and A. Van Proeyen, Off-shell N = (1,0), D = 6 supergravity from superconformal methods, JHEP 02 (2011) 049 [Erratum ibid. 01 (2012) 119] [arXiv:1101.2403] [INSPIRE].
H. Abe, Y. Sakamura and Y. Yamada, N = 1 superfield description of vector-tensor couplings in six dimensions, JHEP 04 (2015) 035 [arXiv:1501.07642] [INSPIRE].
H. Abe, Y. Sakamura and Y. Yamada, N = 1 superfield description of six-dimensional supergravity, JHEP 10 (2015) 181 [arXiv:1507.08435] [INSPIRE].
H. Abe, S. Aoki and Y. Sakamura, Full diffeomorphism and Lorentz invariance in 4D N = 1 superfield description of 6D SUGRA, JHEP 11 (2017) 146 [arXiv:1708.09106] [INSPIRE].
H. Abe and Y. Sakamura, Roles of Z 2 -odd N = 1 multiplets in off-shell dimensional reduction of 5D supergravity, Phys. Rev. D 75 (2007) 025018 [hep-th/0610234] [INSPIRE].
H. Abe and Y. Sakamura, Flavor structure with multi moduli in 5D supergravity, Phys. Rev. D 79 (2009) 045005 [arXiv:0807.3725] [INSPIRE].
H. Abe, H. Otsuka, Y. Sakamura and Y. Yamada, SUSY flavor structure of generic 5D supergravity models, Eur. Phys. J. C 72 (2012) 2018 [arXiv:1111.3721] [INSPIRE].
Y. Sakamura, One-loop Kähler potential in 5D gauged supergravity with generic prepotential, Nucl. Phys. B 873 (2013) 165 [Erratum ibid. B 873 (2013) 728] [arXiv:1302.7244] [INSPIRE].
Y. Sakamura and Y. Yamada, Impacts of non-geometric moduli on effective theory of 5D supergravity, JHEP 11 (2013) 090 [Erratum ibid. 01 (2014) 181] [arXiv:1307.5585] [INSPIRE].
Y. Sakamura and Y. Yamada, Natural realization of a large extra dimension in 5D supersymmetric theory, PTEP 2014 (2014) 093B02 [arXiv:1401.1921] [INSPIRE].
S.M. Carroll and M.M. Guica, Sidestepping the cosmological constant with football shaped extra dimensions, hep-th/0302067 [INSPIRE].
I. Navarro, Codimension two compactifications and the cosmological constant problem, JCAP 09 (2003) 004 [hep-th/0302129] [INSPIRE].
I. Navarro, Spheres, deficit angles and the cosmological constant, Class. Quant. Grav. 20 (2003) 3603 [hep-th/0305014] [INSPIRE].
G.W. Gibbons, R. Güven and C.N. Pope, 3-branes and uniqueness of the Salam-Sezgin vacuum, Phys. Lett. B 595 (2004) 498 [hep-th/0307238] [INSPIRE].
H.M. Lee and C. Lüdeling, The general warped solution with conical branes in six-dimensional supergravity, JHEP 01 (2006) 062 [hep-th/0510026] [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton Univ. Pr., Princeton, U.S.A., (1992) [INSPIRE].
S. Randjbar-Daemi, A. Salam, E. Sezgin and J.A. Strathdee, An anomaly free model in six-dimensions, Phys. Lett. B 151 (1985) 351 [INSPIRE].
M.B. Green, J.H. Schwarz and P.C. West, Anomaly free chiral theories in six-dimensions, Nucl. Phys. B 254 (1985) 327 [INSPIRE].
V. Kumar, D.R. Morrison and W. Taylor, Global aspects of the space of 6D N = 1 supergravities, JHEP 11 (2010) 118 [arXiv:1008.1062] [INSPIRE].
Y. Sakamura, Direct relation of linearized supergravity to superconformal formulation, JHEP 12 (2011) 008 [arXiv:1107.4247] [INSPIRE].
P.A. Horvathy and J.C. Yera, Vortex solutions of the Liouville equation, Lett. Math. Phys. 46 (1998) 111 [hep-th/9805161] [INSPIRE].
M. Redi, Footballs, conical singularities and the Liouville equation, Phys. Rev. D 71 (2005) 044006 [hep-th/0412189] [INSPIRE].
N. Akerblom, G. Cornelissen, G. Stavenga and J.-W. van Holten, Nonrelativistic Chern-Simons vortices on the torus, J. Math. Phys. 52 (2011) 072901 [arXiv:0912.0718] [INSPIRE].
N. Akerblom and G. Cornelissen, A compact codimension two braneworld with precisely one brane, Phys. Rev. D 81 (2010) 124025 [arXiv:1004.1807] [INSPIRE].
A. Salam and E. Sezgin, Chiral compactification on Minkowski ×S 2 of N = 2 Einstein-Maxwell supergravity in six-dimensions, Phys. Lett. B 147 (1984) 47 [INSPIRE].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
P. Olesen, Vacuum structure of the electroweak theory in high magnetic fields, Phys. Lett. B 268 (1991) 389 [INSPIRE].
P. Olesen, Soliton condensation in some selfdual Chern-Simons theories, Phys. Lett. B 265 (1991) 361 [Erratum ibid. B 267 (1991) 541] [INSPIRE].
D. Cremades, L.E. Ibáñez and F. Marchesano, Computing Yukawa couplings from magnetized extra dimensions, JHEP 05 (2004) 079 [hep-th/0404229] [INSPIRE].
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Abe, H., Aoki, S., Imai, S. et al. \( \mathcal{N}=1 \) superfield description of BPS solutions in 6D gauged SUGRA with 3-branes. J. High Energ. Phys. 2018, 73 (2018). https://doi.org/10.1007/JHEP09(2018)073
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DOI: https://doi.org/10.1007/JHEP09(2018)073