Abstract
We study gravitational waves propagating on a warped Minkowski space-time with D − 4 compact extra dimensions. While Kaluza-Klein scales are typically too high for any current detection, we analyse how the warp factor changes the Kaluza-Klein spectrum of gravitational waves. To that end we provide a complete and explicit expression for the warp factor, as well as the Green’s function, on a d-dimensional torus. This expression differs from that of braneworld models and should find further uses in string compactifications. We then evaluate the Kaluza-Klein spectrum of gravitational waves. Our preliminary numerical results indicate not only a deviation from the standard toroidal spectrum, but also that the first masses get lowered due to the warp factor.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
LIGO Scientific and Virgo collaborations, GWTC-1: A Gravitational- Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X 9 (2019) 031040 [arXiv: 1811. 12907] [INSPIRE].
N. Yunes, K. Yagi and F. Pretorius, Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226, Phys. Rev. D 94 (2016) 084002 [arXiv: 1603 .08955] [INSPIRE].
J.M. Ezquiaga and M. Zumalacárregui, Dark Energy After GW170817: Dead Ends and the Road Ahead, Phys. Rev. Lett. 119 (2017) 251304 [arXiv:1710 . 05901] [INSPIRE].
L. Barack et al., Black holes, gravitational waves and fundamental physics: a roadmap, Class. Quant. Grav. 36 (2019) 143001 [arXiv :1806 . 05195] [INSPIRE].
J.M. Ezquiaga and M. Zumalacárregui, Dark Energy in light of Multi-Messenger Gravitational- Wave astronomy, Front. Astron. Space Sci. 5 (2018) 44 [arXiv: 1807. 09241] [INSPIRE].
R. Nair, S. Perkins, H.O. Silva and N. Yunes, Fundamental Physics Implications for Higher-Curvature Theories from Binary Black Hole Signals in the LIGO-Virgo Catalog GWTC-1, Phys. Rev. Lett. 123 (2019) 191101 [arXiv:1905.00870] [INSPIRE].
G. Calcagni, S. Kuroyanagi, S. Marsat, M. Sakellariadou, N. Tamanini and G. Tasinato, Quantum gravity and gravitational-wave astronomy, JCAP 10 (2019) 012 [arXiv:1907.02489] [INSPIRE].
D. Andriot and G. Lucena Gómez, Signatures of extra dimensions in gravitational waves, JCAP 06 (2017) 048 [Erratum ibid. 05 (2019) E01] [arXiv:1704.07392] [INSPIRE].
M. Isi and A.J. WEinstein, Probing gravitational wave polarizations with signals from compact binary coalescences, arXiv:1710.03794 [INSPIRE].
Y. Hagihara, N. Era, D. Iikawa, A. Nishizawa and H. Asada, Constraining extra gravitational wave polarizations with Advanced LIGO, Advanced Virgo and KAGRA and upper bounds from GW170817, Phys. Rev. D 100 (2019) 064010 [arXiv:1904.02300] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence, Phys. Rev. Lett. 119 (2017) 141101 [arXiv:1709.09660] [INSPIRE].
LIGO Scientific and Virgo collaborations, Tests of General Relativity with GW170817, Phys. Rev. Lett. 123 (2019) 011102 [arXiv:1811.00364] [INSPIRE].
R. Brito et al., Gravitational wave searches for ultralight bosons with LIGO and LISA, Phys. Rev. D 96 (2017) 064050 [arXiv:1706.06311] [INSPIRE].
D. Grin et al., Gravitational probes of ultra-light axions, arXiv:1904.09003 [INSPIRE].
L.K. Wong, A.-C. Davis and R. Gregory, Effective field theory for black holes with induced scalar charges, Phys. Rev. D 100 (2019) 024010 [arXiv:1903.07080] [INSPIRE].
V. Cardoso, L. Gualtieri and C.J. Moore, Gravitational waves and higher dimensions: Love numbers and Kaluza-Klein excitations, Phys. Rev. D 100 (2019) 124037 [arXiv:1910.09557] [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].
K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [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].
H. Davoudiasl, J.L. Hewett and T.G. Rizzo, Phenomenology of the Randall-Sundrum Gauge Hierarchy Model, Phys. Rev. Lett. 84 (2000) 2080 [hep-ph/9909255] [INSPIRE].
S.S. Seahra, C. Clarkson and R. Maartens, Detecting extra dimensions with gravity wave spectroscopy: the black string brane-world, Phys. Rev. Lett. 94 (2005) 121302 [gr-qc/0408032] [INSPIRE].
C. Clarkson and S.S. Seahra, A gravitational wave window on extra dimensions, Class. Quant. Grav. 24 (2007) F33 [astro-ph/0610470] [INSPIRE].
B.M. Dillon and V. Sanz, Kaluza-Klein gravitons at LHC2, Phys. Rev. D 96 (2017) 035008 [arXiv:1603.09550] [INSPIRE].
S. Chakraborty, K. Chakravarti, S. Bose and S. SenGupta, Signatures of extra dimensions in gravitational waves from black hole quasinormal modes, Phys. Rev. D 97 (2018) 104053 [arXiv:1710.05188] [INSPIRE].
L. Visinelli, N. Bolis and S. Vagnozzi, Brane-world extra dimensions in light of GW170817, Phys. Rev. D 97 (2018) 064039 [arXiv:1711.06628] [INSPIRE].
D. Andriot, J. Blåbäck and T. Van Riet, Minkowski flux vacua of type-II supergravities, Phys. Rev. Lett. 118 (2017) 011603 [Erratum ibid. 120 (2018) 169901] [arXiv:1609.00729] [INSPIRE].
D. Andriot, New supersymmetric vacua on solvmanifolds, JHEP 02 (2016) 112 [arXiv:1507.00014] [INSPIRE].
N.T. Macpherson and A. Tomasiello, Minimal flux Minkowski classification, JHEP 09 (2017) 126 [arXiv:1612.06885] [INSPIRE].
F. Apruzzi, J.C. Geipel, A. Legramandi, N.T. Macpherson and M. Zagermann, Minkowski4 × S2 solutions of IIB supergravity, Fortsch. Phys. 66 (2018) 1800006 [arXiv:1801.00800] [INSPIRE].
I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting Runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].
C. Córdova, G.B. De Luca and A. Tomasiello, Classical de Sitter Solutions of 10-Dimensional Supergravity, Phys. Rev. Lett. 122 (2019) 091601 [arXiv:1812.04147] [INSPIRE].
F. Carta, J. Moritz and A. Westphal, Gaugino condensation and small uplifts in KKLT, JHEP 08 (2019) 141 [arXiv:1902.01412] [INSPIRE].
R. Blumenhagen, D. Kläwer and L. Schlechter, Swampland Variations on a Theme by KKLT, JHEP 05 (2019) 152 [arXiv:1902.07724] [INSPIRE].
N. Cribiori and D. Junghans, No classical (anti-)de Sitter solutions with O8-planes, Phys. Lett. B 793 (2019) 54 [arXiv:1902.08209] [INSPIRE].
I. Bena, A. Buchel and S. Lüst, Throat destabilization (for profit and for fun), arXiv:1910.08094 [INSPIRE].
C. Bachas and J. Estes, Spin-2 spectrum of defect theories, JHEP 06 (2011) 005 [arXiv:1103.2800] [INSPIRE].
R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1., Wiley, New York (1989).
S. Shandera, B. Shlaer, H. Stoica and S.H.H. Tye, Interbrane interactions in compact spaces and brane inflation, JCAP 02 (2004) 013 [hep-th/0311207] [INSPIRE].
M. Kim and L. McAllister, Monodromy Charge in D7-brane Inflation, arXiv:1812.03532 [INSPIRE].
J.-M. Richard, R. Terrisse and D. Tsimpis, On the spin-2 Kaluza-Klein spectrum of AdS4 × S2 (ℬ4), JHEP 12 (2014) 144 [arXiv:1410.4669] [INSPIRE].
C. Csáki, J. Erlich, T.J. Hollowood and Y. Shirman, Universal aspects of gravity localized on thick branes, Nucl. Phys. B 581 (2000) 309 [hep-th/0001033] [INSPIRE].
M.J. Duff and J.X. Lu, Black and super p-branes in diverse dimensions, Nucl. Phys. B 416 (1994) 301 [hep-th/9306052] [INSPIRE].
D. Youm, Black holes and solitons in string theory, Phys. Rept. 316 (1999) 1 [hep-th/9710046] [INSPIRE].
D. Andriot and J. Blåbäck, Refining the boundaries of the classical de Sitter landscape, JHEP 03 (2017) 102 [Erratum ibid. 03 (2018) 083] [arXiv:1609.00385] [INSPIRE].
C.V. Johnson, D-brane primer, in Strings, branes and gravity. Proceedings, Theoretical Advanced Study Institute, TASI’99, Boulder, U.S.A., 31 May–25 June 1999, pp. 129–350 (2000) [DOI] [hep-th/0007170] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge University Press (2007) [INSPIRE].
C.V. Johnson, Etudes on D-branes, in Nonperturbative aspects of strings, branes and supersymmetry. Proceedings, Spring School on nonperturbative aspects of string theory and supersymmetric gauge theories and Conference on super-five-branes and physics in 5 + 1 dimensions, Trieste, Italy, 23 March–3 April 1998, pp. 75–130 (1998) [hep-th/9812196] [INSPIRE].
H.L. Verlinde, Holography and compactification, Nucl. Phys. B 580 (2000) 264 [hep-th/9906182] [INSPIRE].
D.R. Hartree, The calculation of atomic structures, Wiley, New York, NY (1957).
C. Caprini and D.G. Figueroa, Cosmological Backgrounds of Gravitational Waves, Class. Quant. Grav. 35 (2018) 163001 [arXiv:1801.04268] [INSPIRE].
C. Caprini et al., Reconstructing the spectral shape of a stochastic gravitational wave background with LISA, JCAP 11 (2019) 017 [arXiv:1906.09244] [INSPIRE].
A.R. Frey and A. Maharana, Warped spectroscopy: Localization of frozen bulk modes, JHEP 08 (2006) 021 [hep-th/0603233] [INSPIRE].
C.P. Burgess et al., Warped Supersymmetry Breaking, JHEP 04 (2008) 053 [hep-th/0610255] [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].
D. Junghans, Backreaction of Localised Sources in String Compactifications, Ph.D. Thesis, Leibniz U., Hannover (2013) [arXiv:1309.5990] [INSPIRE].
S. Das, S.S. Haque and B. Underwood, Constraints and horizons for de Sitter with extra dimensions, Phys. Rev. D 100 (2019) 046013 [arXiv:1905.05864] [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].
G. Shiu, G. Torroba, B. Underwood and M.R. Douglas, Dynamics of Warped Flux Compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [INSPIRE].
M.R. Douglas and G. Torroba, Kinetic terms in warped compactifications, JHEP 05 (2009) 013 [arXiv:0805.3700] [INSPIRE].
A.R. Frey, G. Torroba, B. Underwood and M.R. Douglas, The Universal K¨ahler Modulus in Warped Compactifications, JHEP 01 (2009) 036 [arXiv:0810.5768] [INSPIRE].
L. Martucci, On moduli and effective theory of N = 1 warped flux compactifications, JHEP 05 (2009) 027 [arXiv:0902.4031] [INSPIRE].
L. Martucci, Warping the Kähler potential of F-theory/ IIB flux compactifications, JHEP 03 (2015) 067 [arXiv:1411.2623] [INSPIRE].
T.W. Grimm, T.G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher derivative terms — Part I, JHEP 01 (2016) 142 [arXiv:1412.5073] [INSPIRE].
T.W. Grimm, T.G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher-derivative terms — Part II, JHEP 12 (2015) 117 [arXiv:1507.00343] [INSPIRE].
D. Andriot and D. Tsimpis, Laplacian spectrum on a nilmanifold, truncations and effective theories, JHEP 09 (2018) 096 [arXiv:1806.05156] [INSPIRE].
J. Blåbäck, E. van der Woerd, T. Van Riet and M. Williams, Domain walls inside localised orientifolds, JHEP 12 (2015) 078 [arXiv:1510.03984] [INSPIRE].
E. Kiritsis, String theory in a nutshell, Princeton University Press (2007) [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
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1911.01444
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Andriot, D., Tsimpis, D. Gravitational waves in warped compactifications. J. High Energ. Phys. 2020, 100 (2020). https://doi.org/10.1007/JHEP06(2020)100
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)100