Abstract
We study weakly coupled U(1) theories in AdS3, their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together imply the existence of charged operators with conformal dimension significantly below the black hole threshold. We regard this as a form of the Weak Gravity Conjecture (WGC) in three dimensions. We also explore the constraints posed by modular invariance on a particular discrete ℤ N symmetry which arises in our discussion. In this case, modular invariance does not guarantee the existence of light ℤ N -charged states. We also highlight the differences between our discussion and the usual heuristic arguments for the WGC based on black hole remnants.
Article PDF
Avoid common mistakes on your manuscript.
References
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].
T. Rudelius, On the Possibility of Large Axion Moduli Spaces, JCAP 04 (2015) 049 [arXiv:1409.5793] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural Inflation and Quantum Gravity, Phys. Rev. Lett. 114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
T. Rudelius, Constraints on Axion Inflation from the Weak Gravity Conjecture, JCAP 09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP 08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian Axions and the Weak Gravity Conjecture, JHEP 01 (2016) 091 [arXiv:1503.07853] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Winding out of the Swamp: Evading the Weak Gravity Conjecture with F-term Winding Inflation?, Phys. Lett. B 748 (2015) 455 [arXiv:1503.07912] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture, JHEP 04 (2016) 017 [arXiv:1504.00659] [INSPIRE].
D. Junghans, Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture, JHEP 02 (2016) 128 [arXiv:1504.03566] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Weak Gravity Strongly Constrains Large-Field Axion Inflation, JHEP 12 (2015) 108 [arXiv:1506.03447] [INSPIRE].
E. Palti, On Natural Inflation and Moduli Stabilisation in String Theory, JHEP 10 (2015) 188 [arXiv:1508.00009] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Sharpening the Weak Gravity Conjecture with Dimensional Reduction, JHEP 02 (2016) 140 [arXiv:1509.06374] [INSPIRE].
K. Kooner, S. Parameswaran and I. Zavala, Warping the Weak Gravity Conjecture, Phys. Lett. B 759 (2016) 402 [arXiv:1509.07049] [INSPIRE].
R. Kappl, H.P. Nilles and M.W. Winkler, Modulated Natural Inflation, Phys. Lett. B 753 (2016) 653 [arXiv:1511.05560] [INSPIRE].
K. Choi and H. Kim, Aligned natural inflation with modulations, Phys. Lett. B 759 (2016) 520 [arXiv:1511.07201] [INSPIRE].
L.E. Ibáñez, M. Montero, A. Uranga and I. Valenzuela, Relaxion Monodromy and the Weak Gravity Conjecture, JHEP 04 (2016) 020 [arXiv:1512.00025] [INSPIRE].
A. Hebecker, F. Rompineve and A. Westphal, Axion Monodromy and the Weak Gravity Conjecture, JHEP 04 (2016) 157 [arXiv:1512.03768] [INSPIRE].
N. Fonseca, L. de Lima, C.S. Machado and R.D. Matheus, Large field excursions from a few site relaxion model, Phys. Rev. D 94 (2016) 015010 [arXiv:1601.07183] [INSPIRE].
S. Parameswaran, G. Tasinato and I. Zavala, Subleading Effects and the Field Range in Axion Inflation, JCAP 04 (2016) 008 [arXiv:1602.02812] [INSPIRE].
F. Baume and E. Palti, Backreacted Axion Field Ranges in String Theory, JHEP 08 (2016) 043 [arXiv:1602.06517] [INSPIRE].
E. García-Valdecasas and A. Uranga, On the 3-form formulation of axion potentials from D-brane instantons, arXiv:1605.08092 [INSPIRE].
C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
L. Susskind, Trouble for remnants, hep-th/9501106 [INSPIRE].
T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
T. Banks, M. Johnson and A. Shomer, A Note on Gauge Theories Coupled to Gravity, JHEP 09 (2006) 049 [hep-th/0606277] [INSPIRE].
Y. Nakayama and Y. Nomura, Weak gravity conjecture in the AdS/CFT correspondence, Phys. Rev. D 92 (2015) 126006 [arXiv:1509.01647] [INSPIRE].
D. Harlow, Wormholes, Emergent Gauge Fields and the Weak Gravity Conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
G.T. Horowitz, J.E. Santos and B. Way, Evidence for an Electrifying Violation of Cosmic Censorship, Class. Quant. Grav. 33 (2016) 195007 [arXiv:1604.06465] [INSPIRE].
N. Benjamin, E. Dyer, A.L. Fitzpatrick and S. Kachru, Universal Bounds on Charged States in 2d CFT and 3d Gravity, JHEP 08 (2016) 041 [arXiv:1603.09745] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a Lattice Weak Gravity Conjecture, arXiv:1606.08437 [INSPIRE].
J. Griffiths and J. Podolsky, Exact Space-Times in Einstein’s General Relativity, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2009).
T. Ortín, Gravity and strings, Cambridge University Press, Cambridge (2004).
R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1 (1969) 252 [INSPIRE].
R.M. Wald, Gravitational collapse and cosmic censorship, gr-qc/9710068 [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
I. Antoniadis, S. Ferrara, R. Minasian and K.S. Narain, R 4 couplings in M and type-II theories on Calabi-Yau spaces, Nucl. Phys. B 507 (1997) 571 [hep-th/9707013] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the Weak Gravity Conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
S. Deser, R. Jackiw and G. ’t Hooft, Three-Dimensional Einstein Gravity: Dynamics of Flat Space, Annals Phys. 152 (1984) 220 [INSPIRE].
L.E. Ibanez and A.M. Uranga, String theory and particle physics: An introduction to string phenomenology, Cambridge University Press (2012).
F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [INSPIRE].
A.M. Polyakov, Quark Confinement and Topology of Gauge Groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].
I. Affleck, J.A. Harvey, L. Palla and G.W. Semenoff, The Chern-Simons Term Versus the Monopole, Nucl. Phys. B 328 (1989) 575 [INSPIRE].
R. Blumenhagen, M. Cvetič and T. Weigand, Spacetime instanton corrections in 4D string vacua: The seesaw mechanism for D-brane models, Nucl. Phys. B 771 (2007) 113 [hep-th/0609191] [INSPIRE].
L.E. Ibáñez and A.M. Uranga, Neutrino Majorana Masses from String Theory Instanton Effects, JHEP 03 (2007) 052 [hep-th/0609213] [INSPIRE].
B. Florea, S. Kachru, J. McGreevy and N. Saulina, Stringy Instantons and Quiver Gauge Theories, JHEP 05 (2007) 024 [hep-th/0610003] [INSPIRE].
M. Berasaluce-Gonzalez, L.E. Ibáñez, P. Soler and A.M. Uranga, Discrete gauge symmetries in D-brane models, JHEP 12 (2011) 113 [arXiv:1106.4169] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
S. Carlip, The (2+1)-dimensional black hole, Class. Quant. Grav. 12 (1995) 2853 [gr-qc/9506079] [INSPIRE].
D. Birmingham, I. Sachs and S. Sen, Exact results for the BTZ black hole, Int. J. Mod. Phys. D 10 (2001) 833 [hep-th/0102155] [INSPIRE].
S. Carlip, Conformal field theory, (2+1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [INSPIRE].
P. Kraus, Lectures on black holes and the AdS 3 /CF T 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
S. Hyun, G.H. Lee and J.H. Yee, Hawking radiation from (2+1)-dimensional black hole, Phys. Lett. B 322 (1994) 182 [INSPIRE].
S.F. Ross and R.B. Mann, Gravitationally collapsing dust in (2+1)-dimensions, Phys. Rev. D 47 (1993) 3319 [hep-th/9208036] [INSPIRE].
T. Andrade, M. Bañados, R. Benguria and A. Gomberoff, The 2+1 charged black hole in topologically massive electrodynamics, Phys. Rev. Lett. 95 (2005) 021102 [hep-th/0503095] [INSPIRE].
S.R. Coleman, J. Preskill and F. Wilczek, Quantum hair on black holes, Nucl. Phys. B 378 (1992) 175 [hep-th/9201059] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
Y.S. Myung, Phase transition between the BTZ black hole and AdS space, Phys. Lett. B 638 (2006) 515 [gr-qc/0603051] [INSPIRE].
M. Eune, W. Kim and S.-H. Yi, Hawking-Page phase transition in BTZ black hole revisited, JHEP 03 (2013) 020 [arXiv:1301.0395] [INSPIRE].
T. Hartman, Lecture notes on quantum gravity and black holes, (2015) http://www.hartmanhep.net/topics2015/gravity-lectures.pdf.
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge University Press (1998).
P. Goddard and D.I. Olive, Kac-Moody and Virasoro algebras: a reprint volume for physicists, Adv. Ser. Math. Phys. 3 (1988) 1 [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
K. Jensen, Chiral anomalies and AdS/CMT in two dimensions, JHEP 01 (2011) 109 [arXiv:1012.4831] [INSPIRE].
R. Dijkgraaf, J.M. Maldacena, G.W. Moore and E.P. Verlinde, A black hole Farey tail, hep-th/0005003 [INSPIRE].
C.A. Keller and A. Maloney, Poincaré Series, 3D Gravity and CFT Spectroscopy, JHEP 02 (2015) 080 [arXiv:1407.6008] [INSPIRE].
A. Schwimmer and N. Seiberg, Comments on the N = 2, N = 3, N = 4 Superconformal Algebras in Two-Dimensions, Phys. Lett. B 184 (1987) 191 [INSPIRE].
J. Manschot, On the space of elliptic genera, Commun. Num. Theor. Phys. 2 (2008) 803 [arXiv:0805.4333] [INSPIRE].
M.R. Gaberdiel, S. Gukov, C.A. Keller, G.W. Moore and H. Ooguri, Extremal N = (2, 2) 2D Conformal Field Theories and Constraints of Modularity, Commun. Num. Theor. Phys. 2 (2008) 743 [arXiv:0805.4216] [INSPIRE].
W. Van Herck and T. Wyder, Black Hole Meiosis, JHEP 04 (2010) 047 [arXiv:0909.0508] [INSPIRE].
S. Hellerman and C. Schmidt-Colinet, Bounds for State Degeneracies in 2D Conformal Field Theory, JHEP 08 (2011) 127 [arXiv:1007.0756] [INSPIRE].
C.A. Keller, Modularity, Calabi-Yau geometry and 2d CFTs, Proc. Symp. Pure Math. 88 (2014) 307 [arXiv:1312.7313] [INSPIRE].
S. Hellerman, A Universal Inequality for CFT and Quantum Gravity, JHEP 08 (2011) 130 [arXiv:0902.2790] [INSPIRE].
C. Beem, M. Lemos, P. Liendo, L. Rastelli and B.C. van Rees, The \( \mathcal{N}=2 \) superconformal bootstrap, JHEP 03 (2016) 183 [arXiv:1412.7541] [INSPIRE].
J.L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys. B 270 (1986) 186 [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: 1606.08438
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
Montero, M., Shiu, G. & Soler, P. The Weak Gravity Conjecture in three dimensions. J. High Energ. Phys. 2016, 159 (2016). https://doi.org/10.1007/JHEP10(2016)159
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2016)159