Abstract
We study interacting critical UV regime of the long-range O(N) vector model with quartic coupling. Analyzing CFT data within the scope of ϵ- and 1/N-expansion, we collect evidence for the equivalence of this model and the critical IR limit of the cubic model coupled to a generalized free field O(N) vector multiplet.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F.J. Dyson, Existence of a phase transition in a one-dimensional Ising ferromagnet, Commun. Math. Phys. 12 (1969) 91 [INSPIRE].
M.E. Fisher, S.-K. Ma and B.G. Nickel, Critical exponents for long-range interactions, Phys. Rev. Lett. 29 (1972) 917 [INSPIRE].
J.M. Kosterlitz, Phase transitions in long-range ferromagnetic chains, Phys. Rev. Lett. 37 (1976) 1577 [INSPIRE].
M. Aizenman and R. Fernandez, Critical exponents for long-range interactions, Lett. Math. Phys. 16 (1988) 39.
N. Chai, M. Goykhman and R. Sinha, Long-range vector models at large N, arXiv:2107.08052 [INSPIRE].
D.C. Brydges, P.K. Mitter and B. Scoppola, Critical (Φ4)3,ϵ, Commun. Math. Phys. 240 (2003) 281 [hep-th/0206040] [INSPIRE].
A. Abdesselam, A complete renormalization group trajectory between two fixed points, Commun. Math. Phys. 276 (2007) 727 [math-ph/0610018] [INSPIRE].
G. Slade, Critical exponents for long-range O(n) models below the upper critical dimension, Commun. Math. Phys. 358 (2018) 343 [arXiv:1611.06169] [INSPIRE].
D. Benedetti, R. Gurau, S. Harribey and K. Suzuki, Long-range multi-scalar models at three loops, J. Phys. A 53 (2020) 445008 [arXiv:2007.04603] [INSPIRE].
M.F. Paulos, S. Rychkov, B.C. van Rees and B. Zan, Conformal invariance in the long-range Ising model, Nucl. Phys. B 902 (2016) 246 [arXiv:1509.00008] [INSPIRE].
C. Behan, L. Rastelli, S. Rychkov and B. Zan, Long-range critical exponents near the short-range crossover, Phys. Rev. Lett. 118 (2017) 241601 [arXiv:1703.03430] [INSPIRE].
S.S. Gubser, C. Jepsen, S. Parikh and B. Trundy, O(N) and O(N) and O(N), JHEP 11 (2017) 107 [arXiv:1703.04202] [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].
C. Behan, Bootstrapping the long-range Ising model in three dimensions, J. Phys. A 52 (2019) 075401 [arXiv:1810.07199] [INSPIRE].
S. Giombi and H. Khanchandani, O(N) models with boundary interactions and their long range generalizations, JHEP 08 (2020) 010 [arXiv:1912.08169] [INSPIRE].
E. Brezin, G. Parisi and F. Ricci-Tersenghi, The crossover region between long-range and short-range interactions for the critical exponents, Statist. Phys. 5 (2014) 010 [arXiv:1407.3358].
J. Sak, Recursion relations and fixed points for ferromagnets with long-range interactions, Phys. Rev. B 8 (1973) 281.
J. Sak, Low-temperature renormalization group for ferromagnets with long-range interactions, Phys. Rev. B 15 (1977) 4344.
K.G. Wilson and M.E. Fisher, Critical exponents in 3.99 dimensions, Phys. Rev. Lett. 28 (1972) 240 [INSPIRE].
G. Parisi, The theory of nonrenormalizable interactions. 1. The large N expansion, Nucl. Phys. B 100 (1975) 368 [INSPIRE].
L. Fei, S. Giombi and I.R. Klebanov, Critical O(N) models in 6 − ϵ dimensions, Phys. Rev. D 90 (2014) 025018 [arXiv:1404.1094] [INSPIRE].
L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, Three loop analysis of the critical O(N) models in 6 − ϵ dimensions, Phys. Rev. D 91 (2015) 045011 [arXiv:1411.1099] [INSPIRE].
J.A. Gracey, Four loop renormalization of ϕ3 theory in six dimensions, Phys. Rev. D 92 (2015) 025012 [arXiv:1506.03357] [INSPIRE].
J.A. Gracey, Six dimensional QCD at two loops, Phys. Rev. D 93 (2016) 025025 [arXiv:1512.04443] [INSPIRE].
A.C. Petkou, CT and CJ up to next-to-leading order in 1/N in the conformally invariant 0(N) vector model for 2 < d < 4, Phys. Lett. B 359 (1995) 101 [hep-th/9506116] [INSPIRE].
A. Petkou, Conserved currents, consistency relations and operator product expansions in the conformally invariant O(N) vector model, Annals Phys. 249 (1996) 180 [hep-th/9410093] [INSPIRE].
A.N. Vasiliev, Y.M. Pismak and Y.R. Khonkonen, Simple method of calculating the critical indices in the 1/N expansion, Theor. Math. Phys. 46 (1981) 104 [Teor. Mat. Fiz. 46 (1981) 157] [INSPIRE].
A.N. Vasiliev, Y.M. Pismak and Y.R. Khonkonen, 1/N expansion: calculation of the exponents η and ν in the order 1/N2 for arbitrary number of dimensions, Theor. Math. Phys. 47 (1981) 465 [Teor. Mat. Fiz. 47 (1981) 291] [INSPIRE].
M. Goykhman and M. Smolkin, Vector model in various dimensions, Phys. Rev. D 102 (2020) 025003 [arXiv:1911.08298] [INSPIRE].
N. Chai, A. Dymarsky and M. Smolkin, A model of persistent breaking of discrete symmetry, arXiv:2106.09723 [INSPIRE].
N. Chai, S. Chaudhuri, C. Choi, Z. Komargodski, E. Rabinovici and M. Smolkin, Thermal order in conformal theories, Phys. Rev. D 102 (2020) 065014 [arXiv:2005.03676] [INSPIRE].
N. Chai, E. Rabinovici, R. Sinha and M. Smolkin, The bi-conical vector model at 1/N, JHEP 05 (2021) 192 [arXiv:2011.06003] [INSPIRE].
M. D’Eramo, G. Parisi and L. Peliti, Theoretical predictions for critical exponents at the λ-point of Bose liquids, Lett. Nuovo Cim. 2 (1971) 878 [INSPIRE].
K. Symanzik, On calculations in conformal invariant field theories, Lett. Nuovo Cim. 3 (1972) 734 [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: 2108.10084
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
Chakraborty, S., Goykhman, M. Critical long-range vector model in the UV. J. High Energ. Phys. 2021, 151 (2021). https://doi.org/10.1007/JHEP10(2021)151
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2021)151