Abstract
We discuss general supersymmetric brane configurations in flux backgrounds of string and M-theory and derive a necessary condition for the worldvolume theory to be supersymmetric on a given curved manifold. This condition resembles very much the conditions found from coupling a supersymmetric field theory to off-shell supergravity but can be derived in any dimension and for up to sixteen supercharges. Apart from the topological twist, all couplings appearing in the supersymmetry condition are linked to fluxes in the bulk. We explicitly derive the condition for D3-, M2- and M5-branes, in which case the results are also useful for constructing holographic duals to the corresponding field theories. In N = 1 setups we compare the supersymmetry conditions to those that arise by coupling the field theory to off-shell supergravity. We find that the couplings of both old and new minimal supergravity are simultaneously realized, indicating that off-shell supergravity should be coupled via the S-multiplet of 16/16 supergravity in order to describe all supersymmetric brane theories on curved spaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Bershadsky, C. Vafa and V. Sadov, D-branes and topological field theories, Nucl. Phys. B 463 (1996) 420 [hep-th/9511222] [INSPIRE].
E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
J.P. Yamron, Topological actions from twisted supersymmetric theories, Phys. Lett. B 213 (1988) 325 [INSPIRE].
C. Vafa and E. Witten, A strong coupling test of S duality, Nucl. Phys. B 431 (1994) 3 [hep-th/9408074] [INSPIRE].
A. Johansen, Twisting of N = 1 SUSY gauge theories and heterotic topological theories, Int. J. Mod. Phys. A 10 (1995) 4325 [hep-th/9403017] [INSPIRE].
E. Witten, Supersymmetric Yang-Mills theory on a four manifold, J. Math. Phys. 35 (1994) 5101 [hep-th/9403195] [INSPIRE].
A. Adams, H. Jockers, V. Kumar and J.M. Lapan, N = 1 σ-models in AdS 4, JHEP 12 (2011) 042 [arXiv:1104.3155] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
B. Jia and E. Sharpe, Rigidly supersymmetric gauge theories on curved superspace, JHEP 04 (2012) 139 [arXiv:1109.5421] [INSPIRE].
H. Samtleben and D. Tsimpis, Rigid supersymmetric theories in 4D Riemannian space, JHEP 05 (2012) 132 [arXiv:1203.3420] [INSPIRE].
C. Klare, A. Tomasiello and A. Zaffaroni, Supersymmetry on curved spaces and holography, JHEP 08 (2012) 061 [arXiv:1205.1062] [INSPIRE].
T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring curved superspace, JHEP 08 (2012) 141 [arXiv:1205.1115] [INSPIRE].
D. Cassani, C. Klare, D. Martelli, A. Tomasiello and A. Zaffaroni, Supersymmetry in Lorentzian curved spaces and holography, Commun. Math. Phys. 327 (2014) 577 [arXiv:1207.2181] [INSPIRE].
J.T. Liu, L.A. Pando Zayas and D. Reichmann, Rigid supersymmetric backgrounds of minimal off-shell supergravity, JHEP 10 (2012) 034 [arXiv:1207.2785] [INSPIRE].
T.T. Dumitrescu and G. Festuccia, Exploring curved superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric field theories on three-manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].
H. Samtleben, E. Sezgin and D. Tsimpis, Rigid 6D supersymmetry and localization, JHEP 03 (2013) 137 [arXiv:1212.4706] [INSPIRE].
C. Klare and A. Zaffaroni, Extended Supersymmetry on Curved Spaces, JHEP 10 (2013) 218 [arXiv:1308.1102] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The geometry of supersymmetric partition functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, From rigid supersymmetry to twisted holomorphic theories, Phys. Rev. D 90 (2014) 085006 [arXiv:1407.2598] [INSPIRE].
C. Closset and S. Cremonesi, Comments on \( \mathcal{N}=\left(2,2\right) \) supersymmetry on two-manifolds, JHEP 07 (2014) 075 [arXiv:1404.2636] [INSPIRE].
D. Butter, G. Inverso and I. Lodato, Rigid 4D \( \mathcal{N}=2 \) supersymmetric backgrounds and actions, JHEP 09 (2015) 088 [arXiv:1505.03500] [INSPIRE].
A. Lawrence and M. Soroush, N = (4, 4) vector multiplets on curved two-manifolds, arXiv:1509.00890 [INSPIRE].
K.S. Stelle and P.C. West, Minimal auxiliary fields for supergravity, Phys. Lett. B 74 (1978) 330 [INSPIRE].
S. Ferrara and P. van Nieuwenhuizen, The auxiliary fields of supergravity, Phys. Lett. B 74 (1978) 333 [INSPIRE].
M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. B 105 (1981) 353 [INSPIRE].
M. Sohnius and P.C. West, The tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N = 1 supergravity, Nucl. Phys. B 198 (1982) 493 [INSPIRE].
G. Girardi, R. Grimm, M. Muller and J. Wess, Antisymmetric tensor gauge potential in curved superspace and a (16 + 16) supergravity multiplet, Phys. Lett. B 147 (1984) 81 [INSPIRE].
W. Lang, J. Louis and B.A. Ovrut, (16 + 16) supergravity coupled to matter: the low-energy limit of the superstring, Phys. Lett. B 158 (1985) 40 [INSPIRE].
W. Siegel, 16/16 supergravity, Class. Quant. Grav. 3 (1986) L47 [INSPIRE].
M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
P. Koerber, Stable D-branes, calibrations and generalized Calabi-Yau geometry, JHEP 08 (2005) 099 [hep-th/0506154] [INSPIRE].
L. Martucci and P. Smyth, Supersymmetric D-branes and calibrations on general N = 1 backgrounds, JHEP 11 (2005) 048 [hep-th/0507099] [INSPIRE].
L. Martucci, Electrified branes, JHEP 02 (2012) 097 [arXiv:1110.0627] [INSPIRE].
M. Cederwall, A. von Gussich, B.E.W. Nilsson, P. Sundell and A. Westerberg, The Dirichlet super p-branes in ten-dimensional type IIA and IIB supergravity, Nucl. Phys. B 490 (1997) 179 [hep-th/9611159] [INSPIRE].
E. Bergshoeff and P.K. Townsend, Super D-branes, Nucl. Phys. B 490 (1997) 145 [hep-th/9611173] [INSPIRE].
Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
T.T. Dumitrescu and N. Seiberg, Supercurrents and brane currents in diverse dimensions, JHEP 07 (2011) 095 [arXiv:1106.0031] [INSPIRE].
C.M. Hull, Gravitational duality, branes and charges, Nucl. Phys. B 509 (1998) 216 [hep-th/9705162] [INSPIRE].
E. Bergshoeff and J.P. van der Schaar, On M nine-branes, Class. Quant. Grav. 16 (1999) 23 [hep-th/9806069] [INSPIRE].
K. Skenderis and M. Taylor, Branes in AdS and pp wave space-times, JHEP 06 (2002) 025 [hep-th/0204054] [INSPIRE].
H. Lü, C.N. Pope and J. Rahmfeld, A construction of Killing spinors on S n, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
M. Bianchi, A. Collinucci and L. Martucci, Magnetized E3-brane instantons in F-theory, JHEP 12 (2011) 045 [arXiv:1107.3732] [INSPIRE].
M. Bianchi, G. Inverso and L. Martucci, Brane instantons and fluxes in F-theory, JHEP 07 (2013) 037 [arXiv:1212.0024] [INSPIRE].
L. Martucci, Topological duality twist and brane instantons in F-theory, JHEP 06 (2014) 180 [arXiv:1403.2530] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1509.02926
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Triendl, H. Supersymmetric branes on curved spaces and fluxes. J. High Energ. Phys. 2015, 25 (2015). https://doi.org/10.1007/JHEP11(2015)025
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)025