Abstract
We discuss how to incorporate non-supersymmetric branes in compactifications of type II string theories. We particularly focus on flux compactifications on SU(3) × SU(3) structure manifolds to four dimensions, so that a linear \( \mathcal{N} \) = 1 supersymmetry is spontaneously broken by spacetime filling Dp-branes. Anti-Dp-branes are a very special subset of such branes but our analysis is generic. We show that the backreaction of non-supersymmetric branes can be incorporated into the standard 4d \( \mathcal{N} \) = 1 supergravity by including a nilpotent chiral multiplet. Supersymmetry in such setups is always spontaneously broken and non-linearly realized. In particular this means that, contrary to what was previously thought, brane supersymmetry breaking cannot be simply described by a D-term in 4d \( \mathcal{N} \) = 1 supergravity theories.
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References
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].
R. Kallosh and T. Wrase, Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua, JHEP 12 (2014) 117 [arXiv:1411.1121] [INSPIRE].
E.A. Bergshoeff, K. Dasgupta, R. Kallosh, A. Van Proeyen and T. Wrase, \( \overline{D3} \) and dS, JHEP 05 (2015) 058 [arXiv:1502.07627] [INSPIRE].
R. Kallosh, F. Quevedo and A.M. Uranga, String Theory Realizations of the Nilpotent Goldstino, JHEP 12 (2015) 039 [arXiv:1507.07556] [INSPIRE].
I. García-Etxebarria, F. Quevedo and R. Valandro, Global String Embeddings for the Nilpotent Goldstino, JHEP 02 (2016) 148 [arXiv:1512.06926] [INSPIRE].
B. Vercnocke and T. Wrase, Constrained superfields from an anti-D3-brane in KKLT, JHEP 08 (2016) 132 [arXiv:1605.03961] [INSPIRE].
R. Kallosh, B. Vercnocke and T. Wrase, String Theory Origin of Constrained Multiplets, JHEP 09 (2016) 063 [arXiv:1606.09245] [INSPIRE].
L. Aalsma, M. Tournoy, J.P. Van Der Schaar and B. Vercnocke, Supersymmetric embedding of antibrane polarization, Phys. Rev. D 98 (2018) 086019 [arXiv:1807.03303] [INSPIRE].
S. Sugimoto, Anomaly cancellations in type-I D9–\( \overline{D9} \) system and the USp(32) string theory, Prog. Theor. Phys. 102 (1999) 685 [hep-th/9905159] [INSPIRE].
I. Antoniadis, E. Dudas and A. Sagnotti, Brane supersymmetry breaking, Phys. Lett. B 464 (1999) 38 [hep-th/9908023] [INSPIRE].
C. Angelantonj, Comments on open string orbifolds with a nonvanishing Bab , Nucl. Phys. B 566 (2000) 126 [hep-th/9908064] [INSPIRE].
G. Aldazabal and A.M. Uranga, Tachyon free nonsupersymmetric type IIB orientifolds via brane-antibrane systems, JHEP 10 (1999) 024 [hep-th/9908072] [INSPIRE].
C. Angelantonj, I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti, Type I vacua with brane supersymmetry breaking, Nucl. Phys. B 572 (2000) 36 [hep-th/9911081] [INSPIRE].
E. Dudas and J. Mourad, Consistent gravitino couplings in nonsupersymmetric strings, Phys. Lett. B 514 (2001) 173 [hep-th/0012071] [INSPIRE].
G. Pradisi and F. Riccioni, Geometric couplings and brane supersymmetry breaking, Nucl. Phys. B 615 (2001) 33 [hep-th/0107090] [INSPIRE].
J. Mourad and A. Sagnotti, An Update on Brane Supersymmetry Breaking, arXiv:1711.11494 [INSPIRE].
D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [INSPIRE].
R. Kallosh and T. Wrase, dS Supergravity from 10d, Fortsch. Phys. 67 (2019) 1800071 [arXiv:1808.09427] [INSPIRE].
J. Polchinski, String theory. Volume 2: Superstring theory and beyond, in Cambridge Monographs on Mathematical Physics , Cambridge University Press (1998) [INSPIRE].
C.V. Johnson, D-branes, in Cambridge Monographs on Mathematical Physics , Cambridge University Press (2005) [INSPIRE].
M. Cederwall, A. von Gussich, B.E.W. Nilsson and A. Westerberg, The Dirichlet super three-brane in ten-dimensional type IIB supergravity, Nucl. Phys. B 490 (1997) 163 [hep-th/9610148] [INSPIRE].
M. Aganagic, C. Popescu and J.H. Schwarz, D-brane actions with local kappa symmetry, Phys. Lett. B 393 (1997) 311 [hep-th/9610249] [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].
M. Aganagic, C. Popescu and J.H. Schwarz, Gauge invariant and gauge fixed D-brane actions, Nucl. Phys. B 495 (1997) 99 [hep-th/9612080] [INSPIRE].
P. Koerber, Lectures on Generalized Complex Geometry for Physicists, Fortsch. Phys. 59 (2011) 169 [arXiv:1006.1536] [INSPIRE].
N. Cribiori, G. Dall’Agata and F. Farakos, From Linear to Non-linear SUSY and Back Again, JHEP 08 (2017) 117 [arXiv:1704.07387] [INSPIRE].
I. Antoniadis, E. Dudas, S. Ferrara and A. Sagnotti, The Volkov-Akulov-Starobinsky supergravity, Phys. Lett. B 733 (2014) 32 [arXiv:1403.3269] [INSPIRE].
E. Dudas, S. Ferrara, A. Kehagias and A. Sagnotti, Properties of Nilpotent Supergravity, JHEP 09 (2015) 217 [arXiv:1507.07842] [INSPIRE].
E.A. Bergshoeff, D.Z. Freedman, R. Kallosh and A. Van Proeyen, Pure de Sitter Supergravity, Phys. Rev. D 92 (2015) 085040 [Erratum ibid. 93 (2016) 069901] [arXiv:1507.08264] [INSPIRE].
F. Hasegawa and Y. Yamada, Component action of nilpotent multiplet coupled to matter in 4 dimensional \( \mathcal{N} \) = 1 supergravity, JHEP 10 (2015) 106 [arXiv:1507.08619] [INSPIRE].
R. Kallosh, Matter-coupled de Sitter Supergravity, Theor. Math. Phys. 187 (2016) 695 [Teor. Mat. Fiz. 187 (2016) 283] [arXiv:1509.02136] [INSPIRE].
M. Schillo, E. van der Woerd and T. Wrase, The general de Sitter supergravity component action, in The String Theory Universe, proceedings of the 21st European String Workshop and 3rd COST MP1210 Meeting, Leuven, Belgium, 7–11 September 2015, Fortsch. Phys. 64 (2016) 292 [arXiv:1511.01542] [INSPIRE].
D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [Pisma Zh. Eksp. Teor. Fiz. 16 (1972) 621] [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, When does supergravity become strong?, Phys. Lett. B 216 (1989) 325 [Erratum ibid. 229 (1989) 439] [INSPIRE].
R. Kallosh, L. Kofman, A.D. Linde and A. Van Proeyen, Superconformal symmetry, supergravity and cosmology, Class. Quant. Grav. 17 (2000) 4269 [Erratum ibid. 21 (2004) 5017] [hep-th/0006179] [INSPIRE].
G. Dall’Agata and F. Zwirner, On sgoldstino-less supergravity models of inflation, JHEP 12 (2014) 172 [arXiv:1411.2605] [INSPIRE].
S. Ferrara, R. Kallosh and J. Thaler, Cosmology with orthogonal nilpotent superfields, Phys. Rev. D 93 (2016) 043516 [arXiv:1512.00545] [INSPIRE].
J.J.M. Carrasco, R. Kallosh and A.D. Linde, Minimal supergravity inflation, Phys. Rev. D 93 (2016) 061301 [arXiv:1512.00546] [INSPIRE].
S. Ferrara, R. Kallosh, A. Van Proeyen and T. Wrase, Linear Versus Non-linear Supersymmetry, in General, JHEP 04 (2016) 065 [arXiv:1603.02653] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-the/0301240] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
M. Berkooz, M.R. Douglas and R.G. Leigh, Branes intersecting at angles, Nucl. Phys. B 480 (1996) 265 [hep-th/9606139] [INSPIRE].
P. Anastasopoulos, M. Bianchi and R. Richter, Light stringy states, JHEP 03 (2012) 068 [arXiv:1110.5424] [INSPIRE].
P. Anastasopoulos and M. Bianchi, Revisiting light stringy states in view of the 750 GeV diphoton excess, Nucl. Phys. B 911 (2016) 928 [arXiv:1601.07584] [INSPIRE].
M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].
R. Blumenhagen, M. Cvetič, P. Langacker and G. Shiu, Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55 (2005) 71 [hep-th/0502005] [INSPIRE].
L. Aalsma, J.P. van der Schaar and B. Vercnocke, Constrained superfields on metastable anti-D3-branes, JHEP 05 (2017) 089 [arXiv:1703.05771] [INSPIRE].
M.P. Garcia del Moral, S. Parameswaran, N. Quiroz and I. Zavala, Anti-D3 branes and moduli in non-linear supergravity, JHEP 10 (2017) 185 [arXiv:1707.07059] [INSPIRE].
N. Cribiori, C. Roupec, T. Wrase and Y. Yamada, Supersymmetric anti-D3-brane action in the Kachru-Kallosh-Linde-Trivedi setup, Phys. Rev. D 100 (2019) 066001 [arXiv:1906.07727] [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, D-branes on general N = 1 backgrounds: Superpotentials and D-terms, JHEP 06 (2006) 033 [hep-th/0602129] [INSPIRE].
L. Martucci, Electrified branes, JHEP 02 (2012) 097 [arXiv:1110.0627] [INSPIRE].
H. Jockers and J. Louis, The Effective action of D7-branes in N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 705 (2005) 167 [hep-th/0409098] [INSPIRE].
T.W. Grimm and D. Vieira Lopes, The N = 1 effective actions of D-branes in Type IIA and IIB orientifolds, Nucl. Phys. B 855 (2012) 639 [arXiv:1104.2328] [INSPIRE].
M. Kerstan and T. Weigand, The Effective action of D6-branes in N = 1 type IIA orientifolds, JHEP 06 (2011) 105 [arXiv:1104.2329] [INSPIRE].
F. Carta, F. Marchesano, W. Staessens and G. Zoccarato, Open string multi-branched and Kähler potentials, JHEP 09 (2016) 062 [arXiv:1606.00508] [INSPIRE].
D. Escobar, F. Marchesano and W. Staessens, Type IIA Flux Vacua with Mobile D6-branes, JHEP 01 (2019) 096 [arXiv:1811.09282] [INSPIRE].
M. Roček, Linearizing the Volkov-Akulov Model, Phys. Rev. Lett. 41 (1978) 451 [INSPIRE].
S.M. Kuzenko and S.J. Tyler, On the Goldstino actions and their symmetries, JHEP 05 (2011) 055 [arXiv:1102.3043] [INSPIRE].
U. Lindström and M. Roček, Constrained local superfields, Phys. Rev. D 19 (1979) 2300 [INSPIRE].
S. Samuel and J. Wess, A Superfield Formulation of the Nonlinear Realization of Supersymmetry and Its Coupling to Supergravity, Nucl. Phys. B 221 (1983) 153 [INSPIRE].
R. Casalbuoni, S. De Curtis, D. Dominici, F. Feruglio and R. Gatto, Nonlinear Realization of Supersymmetry Algebra From Supersymmetric Constraint, Phys. Lett. B 220 (1989) 569 [INSPIRE].
Z. Komargodski and N. Seiberg, From Linear SUSY to Constrained Superfields, JHEP 09 (2009) 066 [arXiv:0907.2441] [INSPIRE].
S.M. Kuzenko and S.J. Tyler, Complex linear superfield as a model for Goldstino, JHEP 04 (2011) 057 [arXiv:1102.3042] [INSPIRE].
G. Dall’Agata, E. Dudas and F. Farakos, On the origin of constrained superfields, JHEP 05 (2016) 041 [arXiv:1603.03416] [INSPIRE].
I. Bandos, M. Heller, S.M. Kuzenko, L. Martucci and D. Sorokin, The Goldstino brane, the constrained superfields and matter in \( \mathcal{N} \) = 1 supergravity, JHEP 11 (2016) 109 [arXiv:1608.05908] [INSPIRE].
E.I. Buchbinder and S.M. Kuzenko, Three-form multiplet and supersymmetry breaking, JHEP 09 (2017) 089 [arXiv:1705.07700] [INSPIRE].
G. Dall’Agata and F. Farakos, Constrained superfields in Supergravity, JHEP 02 (2016) 101 [arXiv:1512.02158] [INSPIRE].
N. Cribiori, R. Kallosh, C. Roupec and T. Wrase, Uplifting Anti-D6-brane, JHEP 12 (2019) 171 [arXiv:1909.08629] [INSPIRE].
E. McDonough and M. Scalisi, Inflation from Nilpotent Kähler Corrections, JCAP 11 (2016) 028 [arXiv:1609.00364] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].
S. Ferrara, R. Kallosh and A.D. Linde, Cosmology with Nilpotent Superfields, JHEP 10 (2014) 143 [arXiv:1408.4096] [INSPIRE].
G. Villadoro and F. Zwirner, D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications, JHEP 03 (2006) 087 [hep-th/0602120] [INSPIRE].
R. Blumenhagen, V. Braun, B. Körs and D. Lüst, Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes, JHEP 07 (2002) 026 [hep-th/0206038] [INSPIRE].
S. Kachru and J. McGreevy, Supersymmetric three cycles and supersymmetry breaking, Phys. Rev. D 61 (2000) 026001 [hep-th/9908135] [INSPIRE].
M. Cvetič, G. Shiu and A.M. Uranga, Chiral four-dimensional N = 1 supersymmetric type 2A orientifolds from intersecting D6 branes, Nucl. Phys. B 615 (2001) 3 [hep-th/0107166] [INSPIRE].
T.W. Grimm and J. Louis, The Effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [INSPIRE].
E. Palti and T. Weigand, Towards large r from [p, q]-inflation, JHEP 04 (2014) 155 [arXiv:1403.7507] [INSPIRE].
M. Graña, J. Louis and D. Waldram, Hitchin functionals in N = 2 supergravity, JHEP 01 (2006) 008 [hep-th/0505264] [INSPIRE].
I. Benmachiche and T.W. Grimm, Generalized N = 1 orientifold compactifications and the Hitchin functionals, Nucl. Phys. B 748 (2006) 200 [hep-th/0602241] [INSPIRE].
T.W. Grimm and J. Louis, The Effective action of N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 699 (2004) 387 [hep-th/0403067] [INSPIRE].
S. Deser and B. Zumino, Broken Supersymmetry and Supergravity, Phys. Rev. Lett. 38 (1977) 1433 [INSPIRE].
E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys. B 212 (1983) 413 [INSPIRE].
M.T. Grisaru, M. Roček and A. Karlhede, The Superhiggs Effect in Superspace, Phys. Lett. B 120 (1983) 110 [INSPIRE].
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Cribiori, N., Roupec, C., Tournoy, M. et al. Non-supersymmetric branes. J. High Energ. Phys. 2020, 189 (2020). https://doi.org/10.1007/JHEP07(2020)189
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DOI: https://doi.org/10.1007/JHEP07(2020)189