Abstract
We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Simmons-Duffin, The Conformal Bootstrap, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, (2017), pp. 1–74, DOI [arXiv:1602.07982] [INSPIRE].
D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys. 91 (2019) 015002 [arXiv:1805.04405] [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].
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].
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].
M. Montero, G. Shiu and P. Soler, The Weak Gravity Conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP 08 (2017) 025 [arXiv:1606.08437] [INSPIRE].
M. Montero, Are tiny gauge couplings out of the Swampland?, JHEP 10 (2017) 208 [arXiv:1708.02249] [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383 (2021) 1669 [arXiv:1810.05338] [INSPIRE].
J.-B. Bae, S. Lee and J. Song, Modular Constraints on Superconformal Field Theories, JHEP 01 (2019) 209 [arXiv:1811.00976] [INSPIRE].
D. Harlow and H. Ooguri, Constraints on Symmetries from Holography, Phys. Rev. Lett. 122 (2019) 191601 [arXiv:1810.05337] [INSPIRE].
Y.-H. Lin and S.-H. Shao, Anomalies and Bounds on Charged Operators, Phys. Rev. D 100 (2019) 025013 [arXiv:1904.04833] [INSPIRE].
M. Montero, A Holographic Derivation of the Weak Gravity Conjecture, JHEP 03 (2019) 157 [arXiv:1812.03978] [INSPIRE].
J.P. Conlon and F. Quevedo, Putting the Boot into the Swampland, JHEP 03 (2019) 005 [arXiv:1811.06276] [INSPIRE].
J.P. Conlon and F. Revello, Moduli Stabilisation and the Holographic Swampland, LHEP 2020 (2020) 171 [arXiv:2006.01021] [INSPIRE].
H. Ooguri and T. Takayanagi, Cobordism Conjecture in AdS, arXiv:2006.13953 [INSPIRE].
P. Agarwal, K.-H. Lee and J. Song, Classification of large N superconformal gauge theories with a dense spectrum, arXiv:2007.16165 [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].
D. Klaewer and E. Palti, Super-Planckian Spatial Field Variations and Quantum Gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless Strings and the Weak Gravity Conjecture, JHEP 10 (2018) 164 [arXiv:1808.05958] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, A Stringy Test of the Scalar Weak Gravity Conjecture, Nucl. Phys. B 938 (2019) 321 [arXiv:1810.05169] [INSPIRE].
E. Gonzalo, L.E. Ibáñez and A.M. Uranga, Modular symmetries and the swampland conjectures, JHEP 05 (2019) 105 [arXiv:1812.06520] [INSPIRE].
T.W. Grimm, C. Li and E. Palti, Infinite Distance Networks in Field Space and Charge Orbits, JHEP 03 (2019) 016 [arXiv:1811.02571] [INSPIRE].
P. Corvilain, T.W. Grimm and I. Valenzuela, The Swampland Distance Conjecture for Kähler moduli, JHEP 08 (2019) 075 [arXiv:1812.07548] [INSPIRE].
T.W. Grimm and D. Van De Heisteeg, Infinite Distances and the Axion Weak Gravity Conjecture, JHEP 03 (2020) 020 [arXiv:1905.00901] [INSPIRE].
A. Joshi and A. Klemm, Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds, JHEP 08 (2019) 086 [arXiv:1903.00596] [INSPIRE].
F. Marchesano and M. Wiesner, Instantons and infinite distances, JHEP 08 (2019) 088 [arXiv:1904.04848] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions, JHEP 08 (2019) 104 [arXiv:1901.08065] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields, arXiv:1904.06344 [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent Strings from Infinite Distance Limits, arXiv:1910.01135 [INSPIRE].
A. Font, A. Herráez and L.E. Ibáñez, The Swampland Distance Conjecture and Towers of Tensionless Branes, JHEP 08 (2019) 044 [arXiv:1904.05379] [INSPIRE].
F. Baume, F. Marchesano and M. Wiesner, Instanton Corrections and Emergent Strings, JHEP 04 (2020) 174 [arXiv:1912.02218] [INSPIRE].
R. Blumenhagen, I. Valenzuela and F. Wolf, The Swampland Conjecture and F-term Axion Monodromy Inflation, JHEP 07 (2017) 145 [arXiv:1703.05776] [INSPIRE].
R. Blumenhagen, D. Kläwer, L. Schlechter and F. Wolf, The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces, JHEP 06 (2018) 052 [arXiv:1803.04989] [INSPIRE].
D. Erkinger and J. Knapp, Refined swampland distance conjecture and exotic hybrid Calabi-Yaus, JHEP 07 (2019) 029 [arXiv:1905.05225] [INSPIRE].
S. Cecotti, Special Geometry and the Swampland, JHEP 09 (2020) 147 [arXiv:2004.06929] [INSPIRE].
N. Gendler and I. Valenzuela, Merging the weak gravity and distance conjectures using BPS extremal black holes, JHEP 01 (2021) 176 [arXiv:2004.10768] [INSPIRE].
S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela, Swampland Conjectures for Strings and Membranes, JHEP 02 (2021) 006 [arXiv:2006.15154] [INSPIRE].
D. Klaewer, S.-J. Lee, T. Weigand and M. Wiesner, Quantum corrections in 4d N = 1 infinite distance limits and the weak gravity conjecture, JHEP 03 (2021) 252 [arXiv:2011.00024] [INSPIRE].
A. Bedroya and C. Vafa, Trans-Planckian Censorship and the Swampland, JHEP 09 (2020) 123 [arXiv:1909.11063] [INSPIRE].
D. Andriot, N. Cribiori and D. Erkinger, The web of swampland conjectures and the TCC bound, JHEP 07 (2020) 162 [arXiv:2004.00030] [INSPIRE].
A. Bedroya, de Sitter Complementarity, TCC, and the Swampland, arXiv:2010.09760 [INSPIRE].
D. Lüst, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225] [INSPIRE].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents, J. Stat. Phys. 157 (2014) 869 [arXiv:1403.4545] [INSPIRE].
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Precision Islands in the Ising and O(N) Models, JHEP 08 (2016) 036 [arXiv:1603.04436] [INSPIRE].
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT, JHEP 03 (2017) 086 [arXiv:1612.08471] [INSPIRE].
S. Caron-Huot, Y. Gobeil and Z. Zahraee, The leading trajectory in the 2+ 1D Ising CFT, arXiv:2007.11647 [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, The \( \mathcal{N} \) = 4 Superconformal Bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, More \( \mathcal{N} \) = 4 superconformal bootstrap, Phys. Rev. D 96 (2017) 046014 [arXiv:1612.02363] [INSPIRE].
Y.-H. Lin, S.-H. Shao, D. Simmons-Duffin, Y. Wang and X. Yin, \( \mathcal{N} \) = 4 superconformal bootstrap of the K3 CFT, JHEP 05 (2017) 126 [arXiv:1511.04065] [INSPIRE].
C. Behan, Conformal manifolds: ODEs from OPEs, JHEP 03 (2018) 127 [arXiv:1709.03967] [INSPIRE].
V. Bashmakov, M. Bertolini and H. Raj, On non-supersymmetric conformal manifolds: field theory and holography, JHEP 11 (2017) 167 [arXiv:1709.01749] [INSPIRE].
M. Baggio, N. Bobev, S.M. Chester, E. Lauria and S.S. Pufu, Decoding a Three-Dimensional Conformal Manifold, JHEP 02 (2018) 062 [arXiv:1712.02698] [INSPIRE].
J. Kaidi and E. Perlmutter, Discreteness and integrality in Conformal Field Theory, JHEP 02 (2021) 064 [arXiv:2008.02190] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011 [arXiv:1112.1016] [INSPIRE].
M. Kontsevich and Y. Soibelman, Homological mirror symmetry and torus fibrations, in KIAS Annual International Conference on Symplectic Geometry and Mirror Symmetry, (2000), pp. 203–263 [math/0011041] [INSPIRE].
Y. Soibelman, Collapsing conformal field theories and quantum spaces with non-negative ricci curvature, https://www.math.ksu.edu/~soibel/nc-riem-3.pdf.
B.S. Acharya and M.R. Douglas, A finite landscape?, hep-th/0606212 [INSPIRE].
M.R. Douglas, Spaces of Quantum Field Theories, J. Phys. Conf. Ser. 462 (2013) 012011 [arXiv:1005.2779] [INSPIRE].
F. Baume and J. Calderón Infante, Tackling the SDC in AdS with CFTs, JHEP 08 (2021) 057 [arXiv:2011.03583] [INSPIRE].
A.B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
Y.S. Stanev, Constraining conformal field theory with higher spin symmetry in four dimensions, Nucl. Phys. B 876 (2013) 651 [arXiv:1307.5209] [INSPIRE].
N. Boulanger, D. Ponomarev, E.D. Skvortsov and M. Taronna, On the uniqueness of higher-spin symmetries in AdS and CFT, Int. J. Mod. Phys. A 28 (2013) 1350162 [arXiv:1305.5180] [INSPIRE].
T. Hartman, S. Jain and S. Kundu, Causality Constraints in Conformal Field Theory, JHEP 05 (2016) 099 [arXiv:1509.00014] [INSPIRE].
D. Li, D. Meltzer and D. Poland, Conformal Collider Physics from the Lightcone Bootstrap, JHEP 02 (2016) 143 [arXiv:1511.08025] [INSPIRE].
V. Alba and K. Diab, Constraining conformal field theories with a higher spin symmetry in d > 3 dimensions, JHEP 03 (2016) 044 [arXiv:1510.02535] [INSPIRE].
D. Meltzer, Higher Spin ANEC and the Space of CFTs, JHEP 07 (2019) 001 [arXiv:1811.01913] [INSPIRE].
D. Roggenkamp and K. Wendland, Limits and degenerations of unitary conformal field theories, Commun. Math. Phys. 251 (2004) 589 [hep-th/0308143] [INSPIRE].
D. Roggenkamp and K. Wendland, Decoding the geometry of conformal field theories, Bulg. J. Phys. 35 (2008) 139 [arXiv:0803.0657] [INSPIRE].
K. Papadodimas, Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].
D. Anselmi, The N = 4 quantum conformal algebra, Nucl. Phys. B 541 (1999) 369 [hep-th/9809192] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory, in 35th Annual Winter School on Nuclear and Particle Physics, (2001) [hep-ph/0112346] [INSPIRE].
F.A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys. B 629 (2002) 3 [hep-th/0112251] [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
M.S. Costa, T. Hansen and J. Penedones, Bounds for OPE coefficients on the Regge trajectory, JHEP 10 (2017) 197 [arXiv:1707.07689] [INSPIRE].
C. Behan, L. Rastelli, S. Rychkov and B. Zan, A scaling theory for the long-range to short-range crossover and an infrared duality, J. Phys. A 50 (2017) 354002 [arXiv:1703.05325] [INSPIRE].
L. Di Pietro, D. Gaiotto, E. Lauria and J. Wu, 3d Abelian Gauge Theories at the Boundary, JHEP 05 (2019) 091 [arXiv:1902.09567] [INSPIRE].
J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [INSPIRE].
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-Matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
C.-M. Chang and X. Yin, Families of Conformal Fixed Points of N = 2 Chern-Simons-Matter Theories, JHEP 05 (2010) 108 [arXiv:1002.0568] [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ Triality: from Higher Spin Fields to Strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Deformations of Superconformal Theories, JHEP 11 (2016) 135 [arXiv:1602.01217] [INSPIRE].
J. Louis and S. Lüst, Supersymmetric AdS7 backgrounds in half-maximal supergravity and marginal operators of (1, 0) SCFTs, JHEP 10 (2015) 120 [arXiv:1506.08040] [INSPIRE].
W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
V. Asnin, On metric geometry of conformal moduli spaces of four-dimensional superconformal theories, JHEP 09 (2010) 012 [arXiv:0912.2529] [INSPIRE].
F.A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, tt* equations, localization and exact chiral rings in 4d \( \mathcal{N} \) = 2 SCFTs, JHEP 02 (2015) 122 [arXiv:1409.4212] [INSPIRE].
E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere Partition Functions and the Zamolodchikov Metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [INSPIRE].
J. Gomis, P.-S. Hsin, Z. Komargodski, A. Schwimmer, N. Seiberg and S. Theisen, Anomalies, Conformal Manifolds, and Spheres, JHEP 03 (2016) 022 [arXiv:1509.08511] [INSPIRE].
Y. Tachikawa and K. Yonekura, Anomalies involving the space of couplings and the Zamolodchikov metric, JHEP 12 (2017) 140 [arXiv:1710.03934] [INSPIRE].
N. Seiberg, Y. Tachikawa and K. Yonekura, Anomalies of Duality Groups and Extended Conformal Manifolds, PTEP 2018 (2018) 073B04 [arXiv:1803.07366] [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].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, On exact correlation functions in SU(N) \( \mathcal{N} \) = 2 superconformal QCD, JHEP 11 (2015) 198 [arXiv:1508.03077] [INSPIRE].
E. Gerchkovitz, J. Gomis, N. Ishtiaque, A. Karasik, Z. Komargodski and S.S. Pufu, Correlation Functions of Coulomb Branch Operators, JHEP 01 (2017) 103 [arXiv:1602.05971] [INSPIRE].
A. Grassi, Z. Komargodski and L. Tizzano, Extremal correlators and random matrix theory, JHEP 04 (2021) 214 [arXiv:1908.10306] [INSPIRE].
D.A. Kastor, E.J. Martinec and S.H. Shenker, RG Flow in N = 1 Discrete Series, Nucl. Phys. B 316 (1989) 590 [INSPIRE].
P. Meade, N. Seiberg and D. Shih, General Gauge Mediation, Prog. Theor. Phys. Suppl. 177 (2009) 143 [arXiv:0801.3278] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly Marginal Deformations and Global Symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
S.S. Razamat and G. Zafrir, N = 1 conformal dualities, JHEP 09 (2019) 046 [arXiv:1906.05088] [INSPIRE].
S.S. Razamat and G. Zafrir, \( \mathcal{N} \) = 1 conformal duals of gauged En MN models, JHEP 06 (2020) 176 [arXiv:2003.01843] [INSPIRE].
S.S. Razamat, E. Sabag and G. Zafrir, Weakly coupled conformal manifolds in 4d, JHEP 06 (2020) 179 [arXiv:2004.07097] [INSPIRE].
Z. Komargodski, S.S. Razamat, O. Sela and A. Sharon, A Nilpotency Index of Conformal Manifolds, JHEP 10 (2020) 183 [arXiv:2003.04579] [INSPIRE].
O. Aharony, B. Kol and S. Yankielowicz, On exactly marginal deformations of N = 4 SYM and type IIB supergravity on AdS5 × S5, JHEP 06 (2002) 039 [hep-th/0205090] [INSPIRE].
M. Buican and T. Nishinaka, Compact Conformal Manifolds, JHEP 01 (2015) 112 [arXiv:1410.3006] [INSPIRE].
C. Bachas, I. Lavdas and B. Le Floch, Marginal Deformations of 3d N = 4 Linear Quiver Theories, JHEP 10 (2019) 253 [arXiv:1905.06297] [INSPIRE].
E. Beratto, N. Mekareeya and M. Sacchi, Marginal operators and supersymmetry enhancement in 3d S-fold SCFTs, JHEP 12 (2020) 017 [arXiv:2009.10123] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
S.H. Shenker and X. Yin, Vector Models in the Singlet Sector at Finite Temperature, arXiv:1109.3519 [INSPIRE].
S. Giombi and X. Yin, The Higher Spin/Vector Model Duality, J. Phys. A 46 (2013) 214003 [arXiv:1208.4036] [INSPIRE].
V.E. Didenko and E.D. Skvortsov, Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory, JHEP 04 (2013) 158 [arXiv:1210.7963] [INSPIRE].
B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. B Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].
P. Haggi-Mani and B. Sundborg, Free large N supersymmetric Yang-Mills theory as a string theory, JHEP 04 (2000) 031 [hep-th/0002189] [INSPIRE].
E. Sezgin and P. Sundell, Massless higher spins and holography, Nucl. Phys. B 644 (2002) 303 [Erratum ibid. 660 (2003) 403] [hep-th/0205131] [INSPIRE].
M. Bianchi, J.F. Morales and H. Samtleben, On stringy AdS5 × S5 and higher spin holography, JHEP 07 (2003) 062 [hep-th/0305052] [INSPIRE].
N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, On the spectrum of AdS/CFT beyond supergravity, JHEP 02 (2004) 001 [hep-th/0310292] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, String Theory as a Higher Spin Theory, JHEP 09 (2016) 085 [arXiv:1512.07237] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS3, JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboedov, Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude, JHEP 10 (2017) 026 [arXiv:1607.04253] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)/AdS(d+1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
L. Bhardwaj and Y. Tachikawa, Classification of 4d N = 2 gauge theories, JHEP 12 (2013) 100 [arXiv:1309.5160] [INSPIRE].
S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [INSPIRE].
R. Bishop and R.J. Crittenden, Geometry of Manifolds, Pure and applied mathematics, Academic Press, (1964).
M. Cvetič, H. Lü, D.N. Page and C.N. Pope, New Einstein-Sasaki spaces in five and higher dimensions, Phys. Rev. Lett. 95 (2005) 071101 [hep-th/0504225] [INSPIRE].
C. Beem, W. Peelaers, L. Rastelli and B.C. van Rees, Chiral algebras of class S, JHEP 05 (2015) 020 [arXiv:1408.6522] [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
T.W. Grimm, Moduli Space Holography and the Finiteness of Flux Vacua, arXiv:2010.15838 [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, Higher spin symmetry and N = 4 SYM, JHEP 07 (2004) 058 [hep-th/0405057] [INSPIRE].
E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS /CFT correspondence, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2001): Strings, Branes and EXTRA Dimensions, (2002), pp. 3–158 [hep-th/0201253] [INSPIRE].
A. Gadde, E. Pomoni and L. Rastelli, The Veneziano Limit of N = 2 Superconformal QCD: Towards the String Dual of N = 2 SU(N(c)) SYM with N(f) = 2 N(c), arXiv:0912.4918 [INSPIRE].
O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [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: 2011.10040
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
Perlmutter, E., Rastelli, L., Vafa, C. et al. A CFT distance conjecture. J. High Energ. Phys. 2021, 70 (2021). https://doi.org/10.1007/JHEP10(2021)070
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2021)070