Abstract
We argue that the problem of finding lower-dimensional de Sitter solutions to the classical field equations of higher-dimensional supergravity necessarily requires understanding the back-reaction of whatever localized objects source the bulk fields. However, we also find that most of the details of the back-reacted solutions are not important for determining the lower-dimensional curvature. We find, in particular, a classically exact expression that, for a broad class of geometries, directly relates the curvature of the lower-dimensional geometry to asymptotic properties of various bulk fields near the sources. Specializing to codimension-two sources, we find that the contribution involving the asymptotic behaviour of the warp factor (which has a definite sign for most supergravities and so is usually used to infer a preference for anti-de Sitter geometries) is precisely canceled by the contribution of the sources themselves (that are left out in earlier treatments). We identify which combination of bulk fields survives this cancelation, and so controls the sign of the lower-dimensional geometry, for several supergravities in 6, 10 and 11 dimensions. Our results show precisely why explicit 4D de Sitter solutions to 6D supergravity evade general no-go theorems. As an application we show that all classical compactifications of Type IIB supergravity (and F-theory) to 8 dimensions are 8D-flat if they involve only the metric and the axio-dilaton sourced by codimension-two sources, extending earlier results to include warped solutions and more general source properties.
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S.M. Carroll and M.M. Guica, Sidestepping the cosmological constant with football shaped extra dimensions, hep-th/0302067 [INSPIRE].
Y. Aghababaie, C. Burgess, S. Parameswaran and F. Quevedo, SUSY breaking and moduli stabilization from fluxes in gauged 6D supergravity, JHEP 03 (2003) 032 [hep-th/0212091] [INSPIRE].
Y. Aghababaie, C. Burgess, S. Parameswaran and F. Quevedo, Towards a naturally small cosmological constant from branes in 6D supergravity, Nucl. Phys. B 680 (2004) 389 [hep-th/0304256] [INSPIRE].
A.J. Tolley, C. Burgess, D. Hoover and Y. Aghababaie, Bulk singularities and the effective cosmological constant for higher co-dimension branes, JHEP 03 (2006) 091 [hep-th/0512218] [INSPIRE].
G.W. Gibbons, Aspects of supergravity theories, Supersymmetry, supergravity and related topics, in F. del Aguila, J.A. de Azcárraga and L.E. Ibáñez eds., World Scientific, Singapore (1985).
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
D.H. Wesley, Oxidised cosmic acceleration, JCAP 01 (2009) 041 [arXiv:0802.3214] [INSPIRE].
P.J. Steinhardt and D. Wesley, Dark energy, inflation and extra dimensions, Phys. Rev. D 79 (2009) 104026 [arXiv:0811.1614] [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].
C. Burgess, R. Kallosh and F. Quevedo, De Sitter string vacua from supersymmetric D terms, JHEP 10 (2003) 056 [hep-th/0309187] [INSPIRE].
D. Cremades, M.-P. Garcia del Moral, F. Quevedo and K. Suruliz, Moduli stabilisation and de Sitter string vacua from magnetised D7 branes, JHEP 05 (2007) 100 [hep-th/0701154] [INSPIRE].
S. Krippendorf and F. Quevedo, Metastable SUSY breaking, de Sitter moduli stabilisation and Kähler moduli inflation, JHEP 11 (2009) 039 [arXiv:0901.0683] [INSPIRE].
E. Silverstein, Simple de Sitter solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [INSPIRE].
S.S. Haque, G. Shiu, B. Underwood and T. Van Riet, Minimal simple de Sitter solutions, Phys. Rev. D 79 (2009) 086005 [arXiv:0810.5328] [INSPIRE].
T. Wrase and M. Zagermann, On classical de Sitter vacua in string theory, Fortsch. Phys. 58 (2010) 906 [arXiv:1003.0029] [INSPIRE].
U.H. Danielsson, P. Koerber and T. Van Riet, Universal de Sitter solutions at tree-level, JHEP 05 (2010) 090 [arXiv:1003.3590] [INSPIRE].
U.H. Danielsson et al., De Sitter hunting in a classical landscape, Fortsch. Phys. 59 (2011) 897 [arXiv:1103.4858] [INSPIRE].
G. Shiu and Y. Sumitomo, Stability constraints on classical de Sitter vacua, JHEP 09 (2011) 052 [arXiv:1107.2925] [INSPIRE].
S. Weinberg, Gravitation and cosmology, John Wiley & Sons, U.S.A. (1972).
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman and Company, U.S.A. (1973).
H. Nishino and E. Sezgin, The complete N = 2, D = 6 supergravity with matter and Yang-Mills couplings, Nucl. Phys. B 278 (1986) 353 [INSPIRE].
S. Randjbar-Daemi, A. Salam, E. Sezgin and J. Strathdee, An anomaly free model in six-dimensions, Phys. Lett. B 151 (1985) 351 [INSPIRE].
K. Lanczos, Bemerkung zur de Sitterschen Welt (in German), Phys. Z. 23 (1922) 539.
K. Lanczos, Flächenhafte Verteilung der Materie in der Einsteinschen Gravitationstheorie (in German), Ann. Phys. 379 (1924) 518.
C.W. Misner and D.H. Sharp, Relativistic equations for adiabatic, spherically symmetric gravitational collapse, Phys. Rev. 136 (1964) 571.
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuov. Cim. B 44 (1966) 1 [Erratum ibid. B 48 (1966) 463] [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].
L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
W.D. Goldberger and M.B. Wise, Renormalization group flows for brane couplings, Phys. Rev. D 65 (2002) 025011 [hep-th/0104170] [INSPIRE].
E. Dudas, C. Papineau and V. Rubakov, Flowing to four dimensions, JHEP 03 (2006) 085 [hep-th/0512276] [INSPIRE].
C. de Rham, The effective field theory of codimension-two branes, JHEP 01 (2008) 060 [arXiv:0707.0884] [INSPIRE].
C. Burgess, C. de Rham and L. van Nierop, The hierarchy problem and the self-localized Higgs, JHEP 08 (2008) 061 [arXiv:0802.4221] [INSPIRE].
C. Burgess, D. Hoover and G. Tasinato, UV caps and modulus stabilization for 6D gauged chiral supergravity, JHEP 09 (2007) 124 [arXiv:0705.3212] [INSPIRE].
C. Burgess, D. Hoover, C. de Rham and G. Tasinato, Effective field theories and matching for codimension-2 branes, JHEP 03 (2009) 124 [arXiv:0812.3820] [INSPIRE].
P. Bostock, R. Gregory, I. Navarro and J. Santiago, Einstein gravity on the codimension 2-brane?, Phys. Rev. Lett. 92 (2004) 221601 [hep-th/0311074] [INSPIRE].
J. Vinet and J.M. Cline, Codimension-two branes in six-dimensional supergravity and the cosmological constant problem, Phys. Rev. D 71 (2005) 064011 [hep-th/0501098] [INSPIRE].
M. Peloso, L. Sorbo and G. Tasinato, Standard 4D gravity on a brane in six dimensional flux compactifications, Phys. Rev. D 73 (2006) 104025 [hep-th/0603026] [INSPIRE].
B. Himmetoglu and M. Peloso, Isolated Minkowski vacua and stability analysis for an extended brane in the rugby ball, Nucl. Phys. B 773 (2007) 84 [hep-th/0612140] [INSPIRE].
C. de Rham, The effective field theory of codimension-two branes, JHEP 01 (2008) 060 [arXiv:0707.0884] [INSPIRE].
E. Papantonopoulos, A. Papazoglou and V. Zamarias, Regularization of conical singularities in warped six-dimensional compactifications, JHEP 03 (2007) 002 [hep-th/0611311] [INSPIRE].
E. Papantonopoulos, A. Papazoglou and V. Zamarias, Induced cosmology on a regularized brane in six-dimensional flux compactification, Nucl. Phys. B 797 (2008) 520 [arXiv:0707.1396] [INSPIRE].
D. Yamauchi and M. Sasaki, Brane world in arbitrary dimensions without Z 2 symmetry, Prog. Theor. Phys. 118 (2007) 245 [arXiv:0705.2443] [INSPIRE].
N. Kaloper and D. Kiley, Charting the landscape of modified gravity, JHEP 05 (2007) 045 [hep-th/0703190] [INSPIRE].
M. Minamitsuji and D. Langlois, Cosmological evolution of regularized branes in 6D warped flux compactifications, Phys. Rev. D 76 (2007) 084031 [arXiv:0707.1426] [INSPIRE].
S.A. Appleby and R.A. Battye, Regularized braneworlds of arbitrary codimension, Phys. Rev. D 76 (2007) 124009 [arXiv:0707.4238] [INSPIRE].
C. Bogdanos, A. Kehagias and K. Tamvakis, Pseudo-3-branes in a curved 6D bulk, Phys. Lett. B 656 (2007) 112 [arXiv:0709.0873] [INSPIRE].
O. Corradini, K. Koyama and G. Tasinato, Induced gravity on intersecting brane-worlds. Part I. Maximally symmetric solutions, Phys. Rev. D 77 (2008) 084006 [arXiv:0712.0385] [INSPIRE].
F. Arroja, T. Kobayashi, K. Koyama and T. Shiromizu, Low energy effective theory on a regularized brane in 6D gauged chiral supergravity, JCAP 12 (2007) 006 [arXiv:0710.2539] [INSPIRE].
O. Corradini, K. Koyama and G. Tasinato, Induced gravity on intersecting brane-worlds. Part II. Cosmology, Phys. Rev. D 78 (2008) 124002 [arXiv:0803.1850] [INSPIRE].
V. Dzhunushaliev, V. Folomeev and M. Minamitsuji, Thick brane solutions, Rept. Prog. Phys. 73 (2010) 066901 [arXiv:0904.1775] [INSPIRE].
A. Bayntun, C. Burgess and L. van Nierop, Codimension-2 brane-bulk matching: examples from six and ten dimensions, New J. Phys. 12 (2010) 075015 [arXiv:0912.3039] [INSPIRE].
C. Burgess and L. van Nierop, Bulk axions, brane back-reaction and fluxes, JHEP 02 (2011) 094 [arXiv:1012.2638] [INSPIRE].
C. Burgess and L. van Nierop, Large dimensions and small curvatures from supersymmetric brane back-reaction, JHEP 04 (2011) 078 [arXiv:1101.0152] [INSPIRE].
L. van Nierop and C. Burgess, Sculpting the extra dimensions: inflation from codimension-2 brane back-reaction, arXiv:1108.2553 [INSPIRE].
Y. Aghababaie et al., Warped brane worlds in six-dimensional supergravity, JHEP 09 (2003) 037 [hep-th/0308064] [INSPIRE].
E. Witten, Dimensional reduction of superstring models, Phys. Lett. B 155 (1985) 151 [INSPIRE].
C. Burgess, A. Font and F. Quevedo, Low-energy effective action for the superstring, Nucl. Phys. B 272 (1986) 661 [INSPIRE].
B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [INSPIRE].
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
G. Gibbons and S. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [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].
N. Koblitz, Introduction to elliptic curves and modular forms, Springer Verlag, Germany (1984).
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ArXiv ePrint: 1109.0532
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Burgess, C.P., Maharana, A., van Nierop, L. et al. On brane back-reaction and de Sitter solutions in higher-dimensional supergravity. J. High Energ. Phys. 2012, 18 (2012). https://doi.org/10.1007/JHEP04(2012)018
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DOI: https://doi.org/10.1007/JHEP04(2012)018