Abstract
We consider string theory vacua with tadpoles for dynamical fields and uncover universal features of the resulting spacetime-dependent solutions. We argue that the solutions can extend only a finite distance ∆ away in the spacetime dimensions over which the fields vary, scaling as ∆n ∼ \( \mathcal{T} \) with the strength of the tadpole \( \mathcal{T} \). We show that naive singularities arising at this distance scale are physically replaced by ends of spacetime, related to the cobordism defects of the swampland cobordism conjecture and involving stringy ingredients like orientifold planes and branes, or exotic variants thereof. We illustrate these phenomena in large classes of examples, including AdS5 × T1,1 with 3-form fluxes, 10d massive IIA, M-theory on K3, the 10d non-supersymmetric USp(32) strings, and type IIB compactifications with 3-form fluxes and/or magnetized D-branes. We also describe a 6d string model whose tadpole triggers spontaneous compactification to a semirealistic 3-family MSSM-like particle physics model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance, Phys. Lett. B 171 (1986) 383 [INSPIRE].
W. Fischler and L. Susskind, Dilaton Tadpoles, String Condensates and Scale Invariance. 2., Phys. Lett. B 173 (1986) 262 [INSPIRE].
A. Mininno and A.M. Uranga, Dynamical tadpoles and Weak Gravity Constraints, JHEP 05 (2021) 177 [arXiv:2011.00051] [INSPIRE].
S. Sugimoto, Anomaly cancellations in type-I D9-\( \overline{D}9 \) 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].
G. Aldazabal and A.M. Uranga, Tachyon free nonsupersymmetric type IIB orientifolds via brane-antibrane systems, JHEP 10 (1999) 024 [hep-th/9908072] [INSPIRE].
A.M. Uranga, Comments on nonsupersymmetric orientifolds at strong coupling, JHEP 02 (2000) 041 [hep-th/9912145] [INSPIRE].
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007) [DOI] [INSPIRE].
E. Dudas and J. Mourad, Brane solutions in strings with broken supersymmetry and dilaton tadpoles, Phys. Lett. B 486 (2000) 172 [hep-th/0004165] [INSPIRE].
R. Blumenhagen and A. Font, Dilaton tadpoles, warped geometries and large extra dimensions for nonsupersymmetric strings, Nucl. Phys. B 599 (2001) 241 [hep-th/0011269] [INSPIRE].
E. Dudas, J. Mourad and C. Timirgaziu, Time and space dependent backgrounds from nonsupersymmetric strings, Nucl. Phys. B 660 (2003) 3 [hep-th/0209176] [INSPIRE].
E. Dudas, G. Pradisi, M. Nicolosi and A. Sagnotti, On tadpoles and vacuum redefinitions in string theory, Nucl. Phys. B 708 (2005) 3 [hep-th/0410101] [INSPIRE].
J. Mourad and A. Sagnotti, AdS Vacua from Dilaton Tadpoles and Form Fluxes, Phys. Lett. B 768 (2017) 92 [arXiv:1612.08566] [INSPIRE].
J. McNamara and C. Vafa, Cobordism Classes and the Swampland, arXiv:1909.10355 [INSPIRE].
M. Montero and C. Vafa, Cobordism Conjecture, Anomalies, and the String Lamppost Principle, JHEP 01 (2021) 063 [arXiv:2008.11729] [INSPIRE].
M. Dierigl and J.J. Heckman, Swampland cobordism conjecture and non-Abelian duality groups, Phys. Rev. D 103 (2021) 066006 [arXiv:2012.00013] [INSPIRE].
J. Polchinski and E. Witten, Evidence for heterotic — type-I string duality, Nucl. Phys. B 460 (1996) 525 [hep-th/9510169] [INSPIRE].
E. Witten, Strong coupling expansion of Calabi-Yau compactification, Nucl. Phys. B 471 (1996) 135 [hep-th/9602070] [INSPIRE].
D. Lüst, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225] [INSPIRE].
G. Buratti, J. Calderon, A. Mininno and A.M. Uranga, Discrete Symmetries, Weak Coupling Conjecture and Scale Separation in AdS Vacua, JHEP 06 (2020) 083 [arXiv:2003.09740] [INSPIRE].
C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland, and the Missing Corner, PoS TASI2017 (2017) 015 [arXiv:1711.00864] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
M. van Beest, J. Calderón-Infante, D. Mirfendereski and I. Valenzuela, Lectures on the Swampland Program in String Compactifications, arXiv:2102.01111 [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP 08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
S.B. Giddings and A. Strominger, Axion Induced Topology Change in Quantum Gravity and String Theory, Nucl. Phys. B 306 (1988) 890 [INSPIRE].
M. Kruczenski, R.C. Myers and A.W. Peet, Supergravity S-branes, JHEP 05 (2002) 039 [hep-th/0204144] [INSPIRE].
G. Jones, A. Maloney and A. Strominger, Nonsingular solutions for S-branes, Phys. Rev. D 69 (2004) 126008 [hep-th/0403050] [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].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
D.R. Morrison and M.R. Plesser, Nonspherical horizons. 1., Adv. Theor. Math. Phys. 3 (1999) 1 [hep-th/9810201] [INSPIRE].
A.M. Uranga, Brane configurations for branes at conifolds, JHEP 01 (1999) 022 [hep-th/9811004] [INSPIRE].
K. Dasgupta and S. Mukhi, Brane constructions, conifolds and M-theory, Nucl. Phys. B 551 (1999) 204 [hep-th/9811139] [INSPIRE].
G. Buratti, J. Calderón and A.M. Uranga, Transplanckian axion monodromy!?, JHEP 05 (2019) 176 [arXiv:1812.05016] [INSPIRE].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
F. Baume and J. Calderón Infante, Tackling the SDC in AdS with CFTs, arXiv:2011.03583 [INSPIRE].
E. Perlmutter, L. Rastelli, C. Vafa and I. Valenzuela, A CFT Distance Conjecture, arXiv:2011.10040 [INSPIRE].
E. Silverstein and A. Westphal, Monodromy in the CMB: Gravity Waves and String Inflation, Phys. Rev. D 78 (2008) 106003 [arXiv:0803.3085] [INSPIRE].
N. Kaloper and L. Sorbo, A Natural Framework for Chaotic Inflation, Phys. Rev. Lett. 102 (2009) 121301 [arXiv:0811.1989] [INSPIRE].
F. Marchesano, G. Shiu and A.M. Uranga, F-term Axion Monodromy Inflation, JHEP 09 (2014) 184 [arXiv:1404.3040] [INSPIRE].
A. Hebecker, S.C. Kraus and L.T. Witkowski, D7-Brane Chaotic Inflation, Phys. Lett. B 737 (2014) 16 [arXiv:1404.3711] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [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].
A. Hanany and K.D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [INSPIRE].
S. Franco, A. Hanany, K.D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].
K.D. Kennaway, Brane Tilings, Int. J. Mod. Phys. A 22 (2007) 2977 [arXiv:0706.1660] [INSPIRE].
S. Franco, A. Hanany and A.M. Uranga, Multi-flux warped throats and cascading gauge theories, JHEP 09 (2005) 028 [hep-th/0502113] [INSPIRE].
D. Berenstein, C.P. Herzog, P. Ouyang and S. Pinansky, Supersymmetry breaking from a Calabi-Yau singularity, JHEP 09 (2005) 084 [hep-th/0505029] [INSPIRE].
S. Franco, A. Hanany, F. Saad and A.M. Uranga, Fractional branes and dynamical supersymmetry breaking, JHEP 01 (2006) 011 [hep-th/0505040] [INSPIRE].
M. Bertolini, F. Bigazzi and A.L. Cotrone, Supersymmetry breaking at the end of a cascade of Seiberg dualities, Phys. Rev. D 72 (2005) 061902 [hep-th/0505055] [INSPIRE].
K.A. Intriligator and N. Seiberg, The Runaway quiver, JHEP 02 (2006) 031 [hep-th/0512347] [INSPIRE].
G. Buratti, E. García-Valdecasas and A.M. Uranga, Supersymmetry Breaking Warped Throats and the Weak Gravity Conjecture, JHEP 04 (2019) 111 [arXiv:1810.07673] [INSPIRE].
F. Marchesano and G. Shiu, Building MSSM flux vacua, JHEP 11 (2004) 041 [hep-th/0409132] [INSPIRE].
F. Marchesano and G. Shiu, MSSM vacua from flux compactifications, Phys. Rev. D 71 (2005) 011701 [hep-th/0408059] [INSPIRE].
C. Bachas, A Way to break supersymmetry, hep-th/9503030 [INSPIRE].
C. Angelantonj, I. Antoniadis, E. Dudas and A. Sagnotti, Type I strings on magnetized orbifolds and brane transmutation, Phys. Lett. B 489 (2000) 223 [hep-th/0007090] [INSPIRE].
R. Blumenhagen, L. Görlich, B. Körs and D. Lüst, Noncommutative compactifications of type-I strings on tori with magnetic background flux, JHEP 10 (2000) 006 [hep-th/0007024] [INSPIRE].
G. Aldazabal, S. Franco, L.E. Ibáñez, R. Rabadán and A.M. Uranga, D = 4 chiral string compactifications from intersecting branes, J. Math. Phys. 42 (2001) 3103 [hep-th/0011073] [INSPIRE].
G. Aldazabal, S. Franco, L.E. Ibáñez, R. Rabadán and A.M. Uranga, Intersecting brane worlds, JHEP 02 (2001) 047 [hep-ph/0011132] [INSPIRE].
R. Donagi and M. Wijnholt, Model Building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — II: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
R. Blumenhagen, B. Körs and D. Lüst, Type I strings with F flux and B flux, JHEP 02 (2001) 030 [hep-th/0012156] [INSPIRE].
A.M. Uranga, D-brane probes, RR tadpole cancellation and k-theory charge, Nucl. Phys. B 598 (2001) 225 [hep-th/0011048] [INSPIRE].
M. Berkooz, M.R. Douglas and R.G. Leigh, Branes intersecting at angles, Nucl. Phys. B 480 (1996) 265 [hep-th/9606139] [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].
M. Cvetič, G. Shiu and A.M. Uranga, Three family supersymmetric standard-like models from intersecting brane worlds, Phys. Rev. Lett. 87 (2001) 201801 [hep-th/0107143] [INSPIRE].
D. Cremades, L.E. Ibáñez and F. Marchesano, SUSY quivers, intersecting branes and the modest hierarchy problem, JHEP 07 (2002) 009 [hep-th/0201205] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
K. Becker and M. Becker, Supersymmetry breaking, M-theory and fluxes, JHEP 07 (2001) 038 [hep-th/0107044] [INSPIRE].
G. Pradisi and A. Sagnotti, Open String Orbifolds, Phys. Lett. B 216 (1989) 59 [INSPIRE].
E.G. Gimon and J. Polchinski, Consistency conditions for orientifolds and d manifolds, Phys. Rev. D 54 (1996) 1667 [hep-th/9601038] [INSPIRE].
L.J. Romans, Massive N=2a Supergravity in Ten-Dimensions, Phys. Lett. B 169 (1986) 374 [INSPIRE].
E. Bergshoeff, M.B. Green, G. Papadopoulos and P.K. Townsend, The IIA supereight-brane, hep-th/9511079 [INSPIRE].
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
S. Kachru and E. Silverstein, On gauge bosons in the matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70 [hep-th/9612162] [INSPIRE].
P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
R. Antonelli and I. Basile, Brane annihilation in non-supersymmetric strings, JHEP 11 (2019) 021 [arXiv:1908.04352] [INSPIRE].
I. Basile and S. Lanza, de Sitter in non-supersymmetric string theories: no-go theorems and brane-worlds, JHEP 10 (2020) 108 [arXiv:2007.13757] [INSPIRE].
S.S. Razamat and D. Tong, Gapped Chiral Fermions, Phys. Rev. X 11 (2021) 011063 [arXiv:2009.05037] [INSPIRE].
M. Klein and R. Rabadán, ZN × ZM orientifolds with and without discrete torsion, JHEP 10 (2000) 049 [hep-th/0008173] [INSPIRE].
L.E. Ibáñez, F. Marchesano and R. Rabadán, Getting just the standard model at intersecting branes, JHEP 11 (2001) 002 [hep-th/0105155] [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].
V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].
S.S. Gubser and I.R. Klebanov, Baryons and domain walls in an N = 1 superconformal gauge theory, Phys. Rev. D 58 (1998) 125025 [hep-th/9808075] [INSPIRE].
A. Mikhailov, Giant gravitons from holomorphic surfaces, JHEP 11 (2000) 027 [hep-th/0010206] [INSPIRE].
C.E. Beasley, BPS branes from baryons, JHEP 11 (2002) 015 [hep-th/0207125] [INSPIRE].
D. Forcella, I. Garcia-Etxebarria and A. Uranga, E3-brane instantons and baryonic operators for D3-branes on toric singularities, JHEP 03 (2009) 041 [arXiv:0806.2291] [INSPIRE].
A. Hamilton, J. Murugan and A. Prinsloo, Lessons from giant gravitons on AdS5 × T1,1, JHEP 06 (2010) 017 [arXiv:1001.2306] [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
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: 2104.02091
Rights and permissions
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.
About this article
Cite this article
Buratti, G., Delgado, M. & Uranga, A.M. Dynamical tadpoles, stringy cobordism, and the SM from spontaneous compactification. J. High Energ. Phys. 2021, 170 (2021). https://doi.org/10.1007/JHEP06(2021)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2021)170