Abstract
The standard extremal p-brane solutions in supergravity are known to allow for a generalisation which consists of adding a linear dependence on the worldvolume coordinates to the usual harmonic function. In this note we demonstrate that remarkably this generalisation goes through in exactly the same way for p-branes with fluxes added to it that correspond to fractional p-branes. We relate this to warped orientifold compactifications by trading the Dp-branes for Op-planes that solve the RR tadpole condition. This allows us to interpret the worldvolume dependence as due to lower-dimensional scalars that flow along the massless directions in the no-scale potential. Depending on the details of the fluxes these flows can be supersymmetric domain wall flows. Our solutions provide explicit examples of backreacted orientifold planes in compactifications with non-constant moduli.
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S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [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-th/0301240] [INSPIRE].
O. DeWolfe and S.B. Giddings, Scales and hierarchies in warped compactifications and brane worlds, Phys. Rev. D 67 (2003) 066008 [hep-th/0208123] [INSPIRE].
S.B. Giddings and A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape, Phys. Rev. D 73 (2006) 126003 [hep-th/0507158] [INSPIRE].
H. Kodama and K. Uzawa, Comments on the four-dimensional effective theory for warped compactification, JHEP 03 (2006) 053 [hep-th/0512104] [INSPIRE].
K. Koyama, K. Koyama and F. Arroja, On the 4D effective theory in warped compactifications with fluxes and branes, Phys. Lett. B 641 (2006) 81 [hep-th/0607145] [INSPIRE].
A.R. Frey and A. Maharana, Warped spectroscopy: Localization of frozen bulk modes, JHEP 08 (2006) 021 [hep-th/0603233] [INSPIRE].
M.R. Douglas, J. Shelton and G. Torroba, Warping and supersymmetry breaking, arXiv:0704.4001 [INSPIRE].
P. Koerber and L. Martucci, From ten to four and back again: How to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [INSPIRE].
M.R. Douglas and G. Torroba, Kinetic terms in warped compactifications, JHEP 05 (2009) 013 [arXiv:0805.3700] [INSPIRE].
F. Marchesano, P. McGuirk and G. Shiu, Open String Wavefunctions in Warped Compactifications, JHEP 04 (2009) 095 [arXiv:0812.2247] [INSPIRE].
F. Marchesano, P. McGuirk and G. Shiu, Chiral matter wavefunctions in warped compactifications, JHEP 05 (2011) 090 [arXiv:1012.2759] [INSPIRE].
L. Martucci, On moduli and effective theory of N = 1 warped flux compactifications, JHEP 05 (2009) 027 [arXiv:0902.4031] [INSPIRE].
G. Shiu, G. Torroba, B. Underwood and M.R. Douglas, Dynamics of Warped Flux Compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [INSPIRE].
A.R. Frey, G. Torroba, B. Underwood and M.R. Douglas, The Universal Kähler Modulus in Warped Compactifications, JHEP 01 (2009) 036 [arXiv:0810.5768] [INSPIRE].
M.R. Douglas, Effective potential and warp factor dynamics, JHEP 03 (2010) 071 [arXiv:0911.3378] [INSPIRE].
H.-Y. Chen, Y. Nakayama and G. Shiu, On D3-brane Dynamics at Strong Warping, Int. J. Mod. Phys. A 25 (2010) 2493 [arXiv:0905.4463] [INSPIRE].
B. Underwood, A Breathing Mode for Warped Compactifications, Class. Quant. Grav. 28 (2011) 195013 [arXiv:1009.4200] [INSPIRE].
T.W. Grimm, D. Klevers and M. Poretschkin, Fluxes and Warping for Gauge Couplings in F-theory, arXiv:1202.0285 [INSPIRE].
J. Blaback, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].
M.R. Douglas and R. Kallosh, Compactification on negatively curved manifolds, JHEP 06 (2010) 004 [arXiv:1001.4008] [INSPIRE].
H. Kodama and K. Uzawa, Moduli instability in warped compactifications of the type IIB supergravity, JHEP 07 (2005) 061 [hep-th/0504193] [INSPIRE].
P. Binetruy, M. Sasaki and K. Uzawa, Dynamical D4-D8 and D3-D7 branes in supergravity, Phys. Rev. D 80 (2009) 026001 [arXiv:0712.3615] [INSPIRE].
B. Janssen, P. Meessen and T. Ortín, The D8-brane tied up: String and brane solutions in massive type IIA supergravity, Phys. Lett. B 453 (1999) 229 [hep-th/9901078] [INSPIRE].
G. Gibbons, H. Lü and C. Pope, Brane worlds in collision, Phys. Rev. Lett. 94 (2005) 131602 [hep-th/0501117] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N ) × SU(N + M ) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [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. Cvetič, G. Gibbons, H. Lü and C. Pope, Ricci flat metrics, harmonic forms and brane resolutions, Commun. Math. Phys. 232 (2003) 457 [hep-th/0012011] [INSPIRE].
C.P. Herzog and I.R. Klebanov, Gravity duals of fractional branes in various dimensions, Phys. Rev. D 63 (2001) 126005 [hep-th/0101020] [INSPIRE].
F. Saracco and A. Tomasiello, Localized O6-plane solutions with Romans mass, JHEP 07 (2012) 077 [arXiv:1201.5378] [INSPIRE].
R. D’Auria, S. Ferrara, F. Gargiulo, M. Trigiante and S. Vaula, N = 4 supergravity Lagrangian for type IIB on \( {T^6}/{{\mathbb{Z}}_2} \) in presence of fluxes and D3-branes, JHEP 06 (2003) 045 [hep-th/0303049] [INSPIRE].
E. Bergshoeff, M. Nielsen and D. Roest, The Domain walls of gauged maximal supergravities and their M-theory origin, JHEP 07 (2004) 006 [hep-th/0404100] [INSPIRE].
K. Skenderis and P.K. Townsend, Hidden supersymmetry of domain walls and cosmologies, Phys. Rev. Lett. 96 (2006) 191301 [hep-th/0602260] [INSPIRE].
I. Bena, H. Triendl and B. Vercnocke, Camouflaged supersymmetry in solutions of extended supergravities, Phys. Rev. D 86 (2012) 061701 [arXiv:1111.2601] [INSPIRE].
I. Bena, H. Triendl and B. Vercnocke, Black Holes and Fourfolds, JHEP 08 (2012) 124 [arXiv:1206.2349] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A Scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].
J. Blaback, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, The problematic backreaction of SUSY-breaking branes, JHEP 08 (2011) 105 [arXiv:1105.4879] [INSPIRE].
C. Burgess, A. Maharana, L. van Nierop, A. Nizami and F. Quevedo, On Brane Back-Reaction and de Sitter Solutions in Higher-Dimensional Supergravity, JHEP 04 (2012) 018 [arXiv:1109.0532] [INSPIRE].
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ArXiv ePrint: 1207.0814
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Blåbäck, J., Janssen, B., Van Riet, T. et al. Fractional branes, warped compactifications and backreacted orientifold planes. J. High Energ. Phys. 2012, 139 (2012). https://doi.org/10.1007/JHEP10(2012)139
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DOI: https://doi.org/10.1007/JHEP10(2012)139