Abstract
In recent years it has been shown that strongly coupled systems become analytically tractable in the regime of large quantum numbers, such as large spin or large charge. The effective theories that emerge in these two limits are Regge theory and superfluid theory, respectively. Here we make a proposal for a new phase, the “giant vortex,” describing an intermediate regime with large spin and charge. The new phase connects superfluid theory with the large-spin expansion. The giant vortex admits a semi-classical effective theory description with peculiar chiral excitations (moving at the speed of light) and a Fock space of states that is reminiscent of the multi-twist operators in Regge theory, including the leading and daughter Regge trajectories. A similar giant vortex phase appears for Bose-Einstein condensates in a rotating trap, and our results should be applicable in that context as well. We show that the transition from the giant vortex to the Regge regime is accompanied by the scaling dimension turning from being larger than to being smaller than the mean field theory value, i.e. gravity switches from being the weakest force at small AdS distance to being the strongest force at large AdS distance.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S.M. Chester, Weizmann Lectures on the Numerical Conformal Bootstrap, arXiv:1907.05147 [INSPIRE].
S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP 12 (2015) 071 [arXiv:1505.01537] [INSPIRE].
A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data, JHEP 06 (2017) 011 [arXiv:1611.02912] [INSPIRE].
L.A. Gaumé, D. Orlando and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rept. 933 (2021) 1 [arXiv:2008.03308] [INSPIRE].
D. Jafferis, B. Mukhametzhanov and A. Zhiboedov, Conformal Bootstrap At Large Charge, JHEP 05 (2018) 043 [arXiv:1710.11161] [INSPIRE].
G. Badel, G. Cuomo, A. Monin and R. Rattazzi, The Epsilon Expansion Meets Semiclassics, JHEP 11 (2019) 110 [arXiv:1909.01269] [INSPIRE].
L. Alvarez-Gaumé, D. Orlando and S. Reffert, Large charge at large N, JHEP 12 (2019) 142 [arXiv:1909.02571] [INSPIRE].
D. Banerjee, S. Chandrasekharan and D. Orlando, Conformal dimensions via large charge expansion, Phys. Rev. Lett. 120 (2018) 061603 [arXiv:1707.00711] [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [arXiv:0708.0672] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The Analytic Bootstrap and AdS Superhorizon Locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
G. Cuomo, A. de la Fuente, A. Monin, D. Pirtskhalava and R. Rattazzi, Rotating superfluids and spinning charged operators in conformal field theory, Phys. Rev. D 97 (2018) 045012 [arXiv:1711.02108] [INSPIRE].
J.D. Bekenstein and M. Schiffer, The Many faces of superradiance, Phys. Rev. D 58 (1998) 064014 [gr-qc/9803033] [INSPIRE].
K. Kasamatsu, M. Tsubota and M. Ueda, Giant hole and circular superflow in a fast rotating Bose-Einstein condensate, Phys. Rev. A 66 (2002) 053606 [cond-mat/0202223] [INSPIRE].
U.R. Fischer and G. Baym, Vortex states of rapidly rotating dilute Bose-Einstein condensates, Phys. Rev. Lett. 90 (2003) 140402 [cond-mat/0111443] [INSPIRE].
A.L. Fetter, B. Jackson and S. Stringari, Rapid rotation of a bose-einstein condensate in a harmonic plus quartic trap, Physical Review A 71 (2005) .
H. Fu and E. Zaremba, Transition to the giant vortex state in a harmonic-plus-quartic trap, Phys. Rev. A 73 (2006) 013614 [cond-mat/0508515].
A.L. Fetter, Rotating trapped Bose-Einstein condensates, Rev. Mod. Phys. 81 (2009) 647 [INSPIRE].
Y. Guo et al., Supersonic Rotation of a Superfluid: A Long-Lived Dynamical Ring, Phys. Rev. Lett. 124 (2020) 025301 [arXiv:1907.01795].
J.-H. Su, C.-Y. Xia, W.-C. Yang and H.-B. Zeng, Giant vortex in a fast rotating holographic superfluid, arXiv:2208.14172 [INSPIRE].
A.A. Penin and Q. Weller, What Becomes of Giant Vortices in the Abelian Higgs Model, Phys. Rev. Lett. 125 (2020) 251601 [arXiv:2009.06640] [INSPIRE].
A.A. Penin and Q. Weller, A theory of giant vortices, JHEP 08 (2021) 056 [arXiv:2105.12137] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP 08 (2014) 145 [arXiv:1403.6829] [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].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
D. Li, D. Meltzer and D. Poland, Non-Abelian Binding Energies from the Lightcone Bootstrap, JHEP 02 (2016) 149 [arXiv:1510.07044] [INSPIRE].
J. Liu, D. Meltzer, D. Poland and D. Simmons-Duffin, The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT, JHEP 09 (2020) 115 [arXiv:2007.07914] [INSPIRE].
O. Aharony and E. Palti, Convexity of charged operators in CFTs and the weak gravity conjecture, Phys. Rev. D 104 (2021) 126005 [arXiv:2108.04594] [INSPIRE].
O. Antipin, J. Bersini, F. Sannino, Z.-W. Wang and C. Zhang, More on the weak gravity conjecture via convexity of charged operators, JHEP 12 (2021) 204 [arXiv:2109.04946] [INSPIRE].
R. Moser, D. Orlando and S. Reffert, Convexity, large charge and the large-N phase diagram of the φ4 theory, JHEP 02 (2022) 152 [arXiv:2110.07617] [INSPIRE].
E. Palti and A. Sharon, Convexity of charged operators in CFTs with multiple Abelian symmetries, JHEP 09 (2022) 078 [arXiv:2206.06703] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
L. Alberte and A. Nicolis, Spontaneously broken boosts and the Goldstone continuum, JHEP 07 (2020) 076 [arXiv:2001.06024] [INSPIRE].
Z. Komargodski, M. Mezei, S. Pal and A. Raviv-Moshe, Spontaneously broken boosts in CFTs, JHEP 09 (2021) 064 [arXiv:2102.12583] [INSPIRE].
P. Creminelli, O. Janssen and L. Senatore, Positivity bounds on effective field theories with spontaneously broken Lorentz invariance, JHEP 09 (2022) 201 [arXiv:2207.14224] [INSPIRE].
H. Georgi, Generalized dimensional analysis, Phys. Lett. B 298 (1993) 187 [hep-ph/9207278] [INSPIRE].
A. De La Fuente, The large charge expansion at large N , JHEP 08 (2018) 041 [arXiv:1805.00501] [INSPIRE].
G. Badel, E. Firat, A. Monin and R. Rattazzi, Work in progress — Private communication.
G. Badel, A. Monin and R. Rattazzi, Identifying Large Charge Operators, arXiv:2207.08919 [INSPIRE].
L. Onsager, Statistical hydrodynamics, Nuovo Cim. (1943-1954) 6 (1949) 279.
R. Feynman, Chapter II application of quantum mechanics to liquid helium, in Progress in Low Temperature Physics, Elsevier (1955), pp. 17–53 [DOI].
Y. Castin and R. Dum, Bose-Einstein condensates with vortices in rotating traps, European Physical Journal D 7 (1999) 399 [cond-mat/9906144].
A. Aftalion and Q. Du, Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime, Phys. Rev. A 64 (2001) 063603 [cond-mat/0103299].
A. Aftalion, Vortices in Bose-Einstein Condensates, Progress in Nonlinear Differential Equations and Their Applications 67, Birkhäuser Boston (2007) [DOI].
B. Horn, A. Nicolis and R. Penco, Effective string theory for vortex lines in fluids and superfluids, JHEP 10 (2015) 153 [arXiv:1507.05635] [INSPIRE].
N. Sivan and S. Levit, Semiclassical quantization of interacting electrons in a strong magnetic field, Physical Review B 46 (1992) 2319.
A. Entelis and S. Levit, Quantum adiabatic expansion for dynamics in strong magnetic fields, Physical Review Letters 69 (1992) 3001.
T. Tochishita, M. Mizui and H. Kuratsuji, Semiclassical quantization for the motion of the guiding center using the coherent state path integral, Physics Letters A 212 (1996) 304.
G.V. Dunne, R. Jackiw and C.A. Trugenberger, Topological (Chern-Simons) Quantum Mechanics, Phys. Rev. D 41 (1990) 661 [INSPIRE].
G.V. Dunne and R. Jackiw, ‘Peierls substitution’ and Chern-Simons quantum mechanics, Nucl. Phys. B Proc. Suppl. 33 (1993) 114 [hep-th/9204057] [INSPIRE].
Y.M. Shnir, Magnetic Monopoles, Text and Monographs in Physics, Springer Berlin, Heidelberg (2005) [DOI] [INSPIRE].
J. Garaud and A.J. Niemi, Poincaré index formula and analogy with the Kosterlitz-Thouless transition in a non-rotated cold atom Bose-Einstein condensate, JHEP 22 (2020) 154 [arXiv:2108.03155] [INSPIRE].
L. Alvarez-Gaumé, O. Loukas, D. Orlando and S. Reffert, Compensating strong coupling with large charge, JHEP 04 (2017) 059 [arXiv:1610.04495] [INSPIRE].
G. Badel, G. Cuomo, A. Monin and R. Rattazzi, Feynman diagrams and the large charge expansion in 3 ε dimensions, Phys. Lett. B 802 (2020) 135202 [arXiv:1911.08505] [INSPIRE].
G. Cuomo, M. Mezei and A. Raviv-Moshe, Boundary conformal field theory at large charge, JHEP 10 (2021) 143 [arXiv:2108.06579] [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
S.M. Chester et al., Carving out OPE space and precise O(2) model critical exponents, JHEP 06 (2020) 142 [arXiv:1912.03324] [INSPIRE].
S. Viefers, Quantum Hall physics in rotating Bose Einstein condensates, J. Phys. Condens. Matter 20 (2008) 123202 [arXiv:0801.4856].
Y. Nakayama and Y. Nomura, Weak gravity conjecture in the AdS/CFT correspondence, Phys. Rev. D 92 (2015) 126006 [arXiv:1509.01647] [INSPIRE].
S. Hellerman and I. Swanson, String Theory of the Regge Intercept, Phys. Rev. Lett. 114 (2015) 111601 [arXiv:1312.0999] [INSPIRE].
D.T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Annals Phys. 321 (2006) 197 [cond-mat/0509786] [INSPIRE].
S.M. Kravec and S. Pal, Nonrelativistic Conformal Field Theories in the Large Charge Sector, JHEP 02 (2019) 008 [arXiv:1809.08188] [INSPIRE].
S. Hellerman and I. Swanson, Boundary Operators in Effective String Theory, JHEP 04 (2017) 085 [arXiv:1609.01736] [INSPIRE].
S. Hellerman and I. Swanson, Droplet-Edge Operators in Nonrelativistic Conformal Field Theories, arXiv:2010.07967 [INSPIRE].
G. Cuomo, Superfluids, vortices and spinning charged operators in 4d CFT, JHEP 02 (2020) 119 [arXiv:1906.07283] [INSPIRE].
S. Hellerman, S. Maeda and M. Watanabe, Operator Dimensions from Moduli, JHEP 10 (2017) 089 [arXiv:1706.05743] [INSPIRE].
S. Hellerman and S. Maeda, On the Large R-charge Expansion in 𝒩 = 2 Superconformal Field Theories, JHEP 12 (2017) 135 [arXiv:1710.07336] [INSPIRE].
A. Bourget, D. Rodriguez-Gomez and J.G. Russo, A limit for large R-charge correlators in 𝒩 = 2 theories, JHEP 05 (2018) 074 [arXiv:1803.00580] [INSPIRE].
S. Hellerman, S. Maeda, D. Orlando, S. Reffert and M. Watanabe, Universal correlation functions in rank 1 SCFTs, JHEP 12 (2019) 047 [arXiv:1804.01535] [INSPIRE].
M. Beccaria, On the large R-charge 𝒩 = 2 chiral correlators and the Toda equation, JHEP 02 (2019) 009 [arXiv:1809.06280] [INSPIRE].
A. Grassi, Z. Komargodski and L. Tizzano, Extremal correlators and random matrix theory, JHEP 04 (2021) 214 [arXiv:1908.10306] [INSPIRE].
A. Sharon and M. Watanabe, Transition of Large R-Charge Operators on a Conformal Manifold, JHEP 01 (2021) 068 [arXiv:2008.01106] [INSPIRE].
S. Hellerman and D. Orlando, Large R-charge EFT correlators in N = 2 SQCD, arXiv:2103.05642 [INSPIRE].
G. Cuomo, L.V. Delacrétaz and U. Mehta, Large Charge Sector of 3d Parity-Violating CFTs, JHEP 05 (2021) 115 [arXiv:2102.05046] [INSPIRE].
S.M. Kravec and S. Pal, The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals, JHEP 05 (2019) 194 [arXiv:1904.05462] [INSPIRE].
G.F. Cuomo, Large charge, semiclassics and superfluids: from broken symmetries to conformal field theories, Ph.D. Thesis, LPTP, EPFL, Lausanne, Switzerland (2020) [DOI] [INSPIRE].
N. Dondi, I. Kalogerakis, R. Moser, D. Orlando and S. Reffert, Spinning correlators in large-charge CFTs, Nucl. Phys. B 983 (2022) 115928 [arXiv:2203.12624] [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: 2210.15694
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
Cuomo, G., Komargodski, Z. Giant Vortices and the Regge Limit. J. High Energ. Phys. 2023, 6 (2023). https://doi.org/10.1007/JHEP01(2023)006
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2023)006