Abstract
We study how codimension-two objects like vortices back-react gravitationally with their environment in theories (such as 4D or higher-dimensional supergravity) where the bulk is described by a dilaton-Maxwell-Einstein system. We do so both in the full theory, for which the vortex is an explicit classical ‘fat brane’ solution, and in the effective theory of ‘point branes’ appropriate when the vortices are much smaller than the scales of interest for their back-reaction (such as the transverse Kaluza-Klein scale). We extend the standard Nambu-Goto description to include the physics of flux-localization wherein the ambient flux of the external Maxwell field becomes partially localized to the vortex, generalizing the results of a companion paper [10] to include dilaton-dependence for the tension and localized flux. In the effective theory, such flux-localization is described by the next-to-leading effective interaction, and the boundary conditions to which it gives rise are known to play an important role in how (and whether) the vortex causes supersymmetry to break in the bulk. We track how both tension and localized flux determine the curvature of the space-filling dimensions. Our calculations provide the tools required for computing how scale-breaking vortex interactions can stabilize the extra-dimensional size by lifting the dilaton’s flat direction. For small vortices we derive a simple relation between the near-vortex boundary conditions of bulk fields as a function of the tension and localized flux in the vortex action that provides the most efficient means for calculating how physical vortices mutually interact without requiring a complete construction of their internal structure. In passing we show why a common procedure for doing so using a δ-function can lead to incorrect results. Our procedures generalize straightforwardly to general co-dimension objects.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H.B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].
A. Vilenkin and E.P.S. Shellard, Cosmic Strings and other Topological Defects, Cambridge University Press, Cambridge U.K. (1994).
M.B. Hindmarsh and T.W.B. Kibble, Cosmic strings, Rept. Prog. Phys. 58 (1995) 477 [hep-ph/9411342] [INSPIRE].
T. Vachaspati, Dark Strings, Phys. Rev. D 80 (2009) 063502 [arXiv:0902.1764] [INSPIRE].
B. Hartmann and F. Arbabzadah, Cosmic strings interacting with dark strings, JHEP 07 (2009) 068 [arXiv:0904.4591] [INSPIRE].
J.M. Hyde, A.J. Long and T. Vachaspati, Dark Strings and their Couplings to the Standard Model, Phys. Rev. D 89 (2014) 065031 [arXiv:1312.4573] [INSPIRE].
A.J. Long, J.M. Hyde and T. Vachaspati, Cosmic Strings in Hidden Sectors: 1. Radiation of Standard Model Particles, JCAP 09 (2014) 030 [arXiv:1405.7679] [INSPIRE].
P. Arias and F.A. Schaposnik, Vortex solutions of an Abelian Higgs model with visible and hidden sectors, JHEP 12 (2014) 011 [arXiv:1407.2634] [INSPIRE].
H.F. Santana Mota and M. Hindmarsh, Big-Bang Nucleosynthesis and Gamma-Ray Constraints on Cosmic Strings with a large Higgs condensate, Phys. Rev. D 91 (2015) 043001 [arXiv:1407.3599] [INSPIRE].
C.P. Burgess, R. Diener and M. Williams, The Gravity of Dark Vortices: Effective Field Theory for Branes and Strings Carrying Localized Flux, arXiv:1506.08095 [INSPIRE].
H.M. Lee and A. Papazoglou, Supersymmetric codimension-two branes in six-dimensional gauged supergravity, JHEP 01 (2008) 008 [arXiv:0710.4319] [INSPIRE].
C.P. Burgess, L. van Nierop, S. Parameswaran, A. Salvio and M. Williams, Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction, JHEP 02 (2013) 120 [arXiv:1210.5405] [INSPIRE].
C.P. Burgess and L. van Nierop, Bulk Axions, Brane Back-reaction and Fluxes, JHEP 02 (2011) 094 [arXiv:1012.2638] [INSPIRE].
C.P. Burgess and L. van Nierop, Large Dimensions and Small Curvatures from Supersymmetric Brane Back-reaction, JHEP 04 (2011) 078 [arXiv:1101.0152] [INSPIRE].
Y. Aghababaie et al., Warped brane worlds in six-dimensional supergravity, JHEP 09 (2003) 037 [hep-th/0308064] [INSPIRE].
C.P. 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.P. 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].
A. Bayntun, C.P. 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].
R. Diener and C.P. Burgess, Bulk Stabilization, the Extra-Dimensional Higgs Portal and Missing Energy in Higgs Events, JHEP 05 (2013) 078 [arXiv:1302.6486] [INSPIRE].
W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].
Y. Aghababaie, C.P. Burgess, S.L. Parameswaran and F. Quevedo, Towards a naturally small cosmological constant from branes in 6 − D supergravity, Nucl. Phys. B 680 (2004) 389 [hep-th/0304256] [INSPIRE].
C.P. Burgess, Towards a natural theory of dark energy: Supersymmetric large extra dimensions, AIP Conf. Proc. 743 (2005) 417 [hep-th/0411140] [INSPIRE].
C.P. Burgess, Supersymmetric large extra dimensions and the cosmological constant: An Update, Annals Phys. 313 (2004) 283 [hep-th/0402200] [INSPIRE].
C.P. Burgess, The Cosmological Constant Problem: Why it’s hard to get Dark Energy from Micro-physics, arXiv:1309.4133 [INSPIRE].
S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].
E. Witten, The Cosmological constant from the viewpoint of string theory, hep-ph/0002297 [INSPIRE].
J. Polchinski, The Cosmological Constant and the String Landscape, hep-th/0603249 [INSPIRE].
T. Banks, Supersymmetry Breaking and the Cosmological Constant, Int. J. Mod. Phys. A 29 (2014) 1430010 [arXiv:1402.0828] [INSPIRE].
A. Padilla, Lectures on the Cosmological Constant Problem, arXiv:1502.05296 [INSPIRE].
W.D. Goldberger and M.B. Wise, Renormalization group flows for brane couplings, Phys. Rev. D 65 (2002) 025011 [hep-th/0104170] [INSPIRE].
C. de Rham, The Effective field theory of codimension-two branes, JHEP 01 (2008) 060 [arXiv:0707.0884] [INSPIRE].
G.W. Gibbons, R. Güven and C.N. Pope, 3-branes and uniqueness of the Salam-Sezgin vacuum, Phys. Lett. B 595 (2004) 498 [hep-th/0307238] [INSPIRE].
C.P. Burgess, F. Quevedo, G. Tasinato and I. Zavala, General axisymmetric solutions and self-tuning in 6D chiral gauged supergravity, JHEP 11 (2004) 069 [hep-th/0408109] [INSPIRE].
C.P. Burgess, L. van Nierop and M. Williams, Distributed SUSY breaking: dark energy, Newton’s law and the LHC, JHEP 07 (2014) 034 [arXiv:1311.3911] [INSPIRE].
S. Weinberg, Gravitation and Cosmology, Wiley, New York U.S.A. (1973).
C.W. Misner, J.A. Wheeler and K.S. Thorne, Gravitation, W.H. Freeman & Company, New York 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.A. Strathdee, An Anomaly Free Model in Six-Dimensions, Phys. Lett. B 151 (1985) 351 [INSPIRE].
A.J. Tolley, C.P. 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].
E.M. Lifshitz and I.M. Khalatnikov, Investigations in relativistic cosmology, Adv. Phys. 12 (1963) 185.
V.A. Belinsky, I.M. Khalatnikov and E.M. Lifshitz, Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys. 19 (1970) 525 [Sov. Phys. JETP 36 (1973) 591] [INSPIRE].
E. Kasner, Solution of the Einstein equations involving functions of only one variable, Trans. Amer. Math. Soc. 27 (1925) 155.
H.M. Lee and A. Papazoglou, Scalar mode analysis of the warped Salam-Sezgin model, Nucl. Phys. B 747 (2006) 294 [Erratum ibid. B 765 (2007) 200] [hep-th/0602208] [INSPIRE].
C.P. Burgess, C. de Rham, D. Hoover, D. Mason and A.J. Tolley, Kicking the rugby ball: Perturbations of 6D gauged chiral supergravity, JCAP 02 (2007) 009 [hep-th/0610078] [INSPIRE].
A. Salvio, Aspects of physics with two extra dimensions, hep-th/0701020 [INSPIRE].
A. Salvio, Brane Gravitational Interactions from 6D Supergravity, Phys. Lett. B 681 (2009) 166 [arXiv:0909.0023] [INSPIRE].
C.P. Burgess, L. van Nierop and M. Williams, Gravitational Forces on a Codimension-2 Brane, JHEP 04 (2014) 032 [arXiv:1401.0511] [INSPIRE].
A.J. Tolley, C.P. Burgess, C. de Rham and D. Hoover, Scaling solutions to 6D gauged chiral supergravity, New J. Phys. 8 (2006) 324 [hep-th/0608083] [INSPIRE].
L. van Nierop and C.P. Burgess, Sculpting the Extra Dimensions: Inflation from Codimension-2 Brane Back-reaction, JCAP 04 (2012) 037 [arXiv:1108.2553] [INSPIRE].
C.P. Burgess, A. Maharana, L. van Nierop, A.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].
F.F. Gautason, D. Junghans and M. Zagermann, Cosmological Constant, Near Brane Behavior and Singularities, JHEP 09 (2013) 123 [arXiv:1301.5647] [INSPIRE].
R. Koster and M. Postma, A no-go for no-go theorems prohibiting cosmic acceleration in extra dimensional models, JCAP 12 (2011) 015 [arXiv:1110.1492] [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 16 (2001) 822 [hep-th/0007018] [INSPIRE].
D.H. Wesley, New no-go theorems for cosmic acceleration with extra dimensions, arXiv:0802.2106 [INSPIRE].
P.J. Steinhardt and D. Wesley, Dark Energy, Inflation and Extra Dimensions, Phys. Rev. D 79 (2009) 104026 [arXiv:0811.1614] [INSPIRE].
S.L. Parameswaran, G. Tasinato and I. Zavala, The 6D SuperSwirl, Nucl. Phys. B 737 (2006) 49 [hep-th/0509061] [INSPIRE].
E.J. Copeland and O. Seto, Dynamical solutions of warped six dimensional supergravity, JHEP 08 (2007) 001 [arXiv:0705.4169] [INSPIRE].
A.J. Tolley, C.P. Burgess, C. de Rham and D. Hoover, Exact Wave Solutions to 6D Gauged Chiral Supergravity, JHEP 07 (2008) 075 [arXiv:0710.3769] [INSPIRE].
M. Minamitsuji, Instability of brane cosmological solutions with flux compactifications, Class. Quant. Grav. 25 (2008) 075019 [arXiv:0801.3080] [INSPIRE].
H.M. Lee and A. Papazoglou, Codimension-2 brane inflation, Phys. Rev. D 80 (2009) 043506 [arXiv:0901.4962] [INSPIRE].
H.M. Lee and C. Lüdeling, The General warped solution with conical branes in six-dimensional supergravity, JHEP 01 (2006) 062 [hep-th/0510026] [INSPIRE].
N. Kaloper and D. Kiley, Exact black holes and gravitational shockwaves on codimension-2 branes, JHEP 03 (2006) 077 [hep-th/0601110] [INSPIRE].
A. Vilenkin, Gravitational Field of Vacuum Domain Walls and Strings, Phys. Rev. D 23 (1981) 852 [INSPIRE].
D. Garfinkle, General Relativistic Strings, Phys. Rev. D 32 (1985) 1323 [INSPIRE].
P. Laguna-Castillo and R.A. Matzner, Coupled Field Solutions for U(1) Gauge Cosmic Strings, Phys. Rev. D 36 (1987) 3663 [INSPIRE].
R. Gregory, Gravitational Stability of Local Strings, Phys. Rev. Lett. 59 (1987) 740 [INSPIRE].
R. Gregory, Effective Action for a Cosmic String, Phys. Lett. B 206 (1988) 199 [INSPIRE].
R. Gregory, D. Haws and D. Garfinkle, The Dynamics of Domain Walls and Strings, Phys. Rev. D 42 (1990) 343 [INSPIRE].
C.P. Burgess, R. Diener and M. Williams, Self-Tuning at Large (Distances): 4D Description of Runaway Dilaton Capture, JHEP 10 (2015) 177 [arXiv:1509.04209] [INSPIRE].
A. Salam and E. Sezgin, Chiral Compactification on Minkowski X S 2 of N = 2 Einstein-Maxwell Supergravity in Six-Dimensions, Phys. Lett. B 147 (1984) 47 [INSPIRE].
T. Gherghetta, E. Roessl and M.E. Shaposhnikov, Living inside a hedgehog: Higher dimensional solutions that localize gravity, Phys. Lett. B 491 (2000) 353 [hep-th/0006251] [INSPIRE].
T. Gherghetta and M.E. Shaposhnikov, Localizing gravity on a string-like defect in six-dimensions, Phys. Rev. Lett. 85 (2000) 240 [hep-th/0004014] [INSPIRE].
B. Holdom, Two U(1)’s and Epsilon Charge Shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].
C.P. Burgess, R.C. Myers and F. Quevedo, A Naturally small cosmological constant on the brane?, Phys. Lett. B 495 (2000) 384 [hep-th/9911164] [INSPIRE].
F. Niedermann and R. Schneider, Fine-tuning with Brane-Localized Flux in 6D Supergravity, arXiv:1508.01124 [INSPIRE].
F. Niedermann and R. Schneider, Fine-tuning with Brane-Localized Flux in 6D Supergravity, arXiv:1508.01124 [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: 1508.00856
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
Burgess, C.P., Diener, R. & Williams, M. EFT for vortices with dilaton-dependent localized flux. J. High Energ. Phys. 2015, 54 (2015). https://doi.org/10.1007/JHEP11(2015)054
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)054