Abstract
We discuss non-linear instantons in supersymmetric field theories on curved spaces arising from D-branes. Focussing on D3-branes and four-dimensional field theories, we derive the supersymmetry conditions and show the intimate relation between the instanton solutions and the non-linearly realized supersymmetries of the field theory. We demonstrate that field theories with non-linearly realized supersymmetries are coupled to supergravity backgrounds in a similar fashion as those with linearly realized supersymmetries, and provide details on how to derive such couplings from a type II perspective.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
H. Samtleben and D. Tsimpis, Rigid supersymmetric theories in 4d Riemannian space, JHEP 05 (2012) 132 [arXiv:1203.3420] [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].
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].
T.T. Dumitrescu and G. Festuccia, Exploring curved superspace (II), JHEP 01 (2013) 072 [arXiv:1209.5408] [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].
B. Jia and E. Sharpe, Rigidly supersymmetric gauge theories on curved superspace, JHEP 04 (2012) 139 [arXiv:1109.5421] [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].
H. Triendl, Supersymmetric branes on curved spaces and fluxes, JHEP 11 (2015) 025 [arXiv:1509.02926] [INSPIRE].
T. Maxfield, D. Robbins and S. Sethi, A landscape of field theories, JHEP 11 (2016) 162 [arXiv:1512.03999] [INSPIRE].
C. Hull and H. Triendl, Conformal branes and their coupling to the Weyl multiplet, to appear.
J. Hughes and J. Polchinski, Partially broken global supersymmetry and the superstring, Nucl. Phys. B 278 (1986) 147 [INSPIRE].
I. Antoniadis, H. Partouche and T.R. Taylor, Spontaneous breaking of N = 2 global supersymmetry, Phys. Lett. B 372 (1996) 83 [hep-th/9512006] [INSPIRE].
J. Bagger and A. Galperin, A new Goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177] [INSPIRE].
M. Roček and A.A. Tseytlin, Partial breaking of global D = 4 supersymmetry, constrained superfields and three-brane actions, Phys. Rev. D 59 (1999) 106001 [hep-th/9811232] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
M. Mariño, R. Minasian, G.W. Moore and A. Strominger, Nonlinear instantons from supersymmetric p-branes, JHEP 01 (2000) 005 [hep-th/9911206] [INSPIRE].
E. Bergshoeff, M.J. Duff, C.N. Pope and E. Sezgin, Supersymmetric supermembrane vacua and singletons, Phys. Lett. B 199 (1987) 69 [INSPIRE].
K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].
P.S. Aspinwall, K3 surfaces and string duality, in Differential geometry inspired by string theory, S.T. Yau ed., International Press, Boston U.S.A., (1999), pg. 1 [hep-th/9611137] [INSPIRE].
D. Prins and D. Tsimpis, Type IIA supergravity and M-theory on manifolds with SU(4) structure, Phys. Rev. D 89 (2014) 064030 [arXiv:1312.1692] [INSPIRE].
H. Samtleben, E. Sezgin and D. Tsimpis, Rigid 6D supersymmetry and localization, JHEP 03 (2013) 137 [arXiv:1212.4706] [INSPIRE].
T. Maxfield, Supergravity backgrounds for four-dimensional maximally supersymmetric Yang-Mills, JHEP 02 (2017) 065 [arXiv:1609.05905] [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].
B. de Wit and H. Nicolai, d = 11 supergravity with local SU(8) invariance, Nucl. Phys. B 274 (1986) 363 [INSPIRE].
B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [INSPIRE].
B. de Wit and H. Nicolai, The consistency of the S 7 truncation in D = 11 supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, The maximal D = 4 supergravities, JHEP 06 (2007) 049 [arXiv:0705.2101] [INSPIRE].
P. de Medeiros, Rigid supersymmetry, conformal coupling and twistor spinors, JHEP 09 (2014) 032 [arXiv:1209.4043] [INSPIRE].
H. Baum, Holonomy groups of Lorentzian manifolds: a status report, Springer Proc. Math. 17 (2012) 163 [INSPIRE].
L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [INSPIRE].
A. Butti, M. Graña, R. Minasian, M. Petrini and A. Zaffaroni, The baryonic branch of Klebanov-Strassler solution: a supersymmetric family of SU(3) structure backgrounds, JHEP 03 (2005) 069 [hep-th/0412187] [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. Graña and J. Polchinski, Gauge/gravity duals with holomorphic dilaton, Phys. Rev. D 65 (2002) 126005 [hep-th/0106014] [INSPIRE].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
J.-M. Bismut, A local index theorem for non Kähler manifolds, Math. Ann. 284 (1989) 681.
A. Coimbra, R. Minasian, H. Triendl and D. Waldram, Generalised geometry for string corrections, JHEP 11 (2014) 160 [arXiv:1407.7542] [INSPIRE].
A. Coimbra and R. Minasian, M-theoretic Lichnerowicz formula and supersymmetry, arXiv:1705.04330 [INSPIRE].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [INSPIRE].
D. Lüst, P. Patalong and D. Tsimpis, Generalized geometry, calibrations and supersymmetry in diverse dimensions, JHEP 01 (2011) 063 [arXiv:1010.5789] [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: 1707.07002
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
Minasian, R., Prins, D. & Triendl, H. Supersymmetric branes and instantons on curved spaces. J. High Energ. Phys. 2017, 159 (2017). https://doi.org/10.1007/JHEP10(2017)159
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)159