Abstract
We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.
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References
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
V.S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions, Phys. Rev. D 80 (2009) 045006 [arXiv:0905.2211] [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].
S.M. Chester, Weizmann Lectures on the Numerical Conformal Bootstrap, arXiv:1907.05147 [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping Mixed Correlators in the 3D Ising Model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Bootstrapping the O(N ) Archipelago, JHEP 11 (2015) 106 [arXiv:1504.07997] [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].
J. Rong and N. Su, Bootstrapping minimal \( \mathcal{N} \) = 1 superconformal field theory in three dimensions, arXiv:1807.04434 [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, The M-theory Archipelago, JHEP 02 (2020) 010 [arXiv:1907.13222] [INSPIRE].
Z. Li and N. Su, Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N ) Models, JHEP 04 (2017) 098 [arXiv:1607.07077] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Conformal Bootstrap Dashing Hopes of Emergent Symmetry, Phys. Rev. Lett. 117 (2016) 131601 [arXiv:1602.07295] [INSPIRE].
D. Li, D. Meltzer and A. Stergiou, Bootstrapping mixed correlators in 4D \( \mathcal{N} \) = 1 SCFTs, JHEP 07 (2017) 029 [arXiv:1702.00404] [INSPIRE].
C. Behan, Bootstrapping the long-range Ising model in three dimensions, J. Phys. A 52 (2019) 075401 [arXiv:1810.07199] [INSPIRE].
S.R. Kousvos and A. Stergiou, Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories, SciPost Phys. 6 (2019) 035 [arXiv:1810.10015] [INSPIRE].
S.R. Kousvos and A. Stergiou, Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II, arXiv:1911.00522 [INSPIRE].
L. Iliesiu, F. Kos, D. Poland, S.S. Pufu, D. Simmons-Duffin and R. Yacoby, Bootstrapping 3D Fermions, JHEP 03 (2016) 120 [arXiv:1508.00012] [INSPIRE].
L. Iliesiu, F. Kos, D. Poland, S.S. Pufu and D. Simmons-Duffin, Bootstrapping 3D Fermions with Global Symmetries, JHEP 01 (2018) 036 [arXiv:1705.03484] [INSPIRE].
D. Karateev, P. Kravchuk, M. Serone and A. Vichi, Fermion Conformal Bootstrap in 4d, JHEP 06 (2019) 088 [arXiv:1902.05969] [INSPIRE].
A. Dymarsky, J. Penedones, E. Trevisani and A. Vichi, Charting the space of 3D CFTs with a continuous global symmetry, JHEP 05 (2019) 098 [arXiv:1705.04278] [INSPIRE].
M. Reehorst, E. Trevisani and A. Vichi, Mixed Scalar-Current bootstrap in three dimensions, arXiv:1911.05747 [INSPIRE].
A. Dymarsky, F. Kos, P. Kravchuk, D. Poland and D. Simmons-Duffin, The 3d Stress-Tensor Bootstrap, JHEP 02 (2018) 164 [arXiv:1708.05718] [INSPIRE].
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D Conformal Field Theories with Global Symmetry, J. Phys. A 44 (2011) 035402 [arXiv:1009.5985] [INSPIRE].
A. Vichi, Improved bounds for CFT’s with global symmetries, JHEP 01 (2012) 162 [arXiv:1106.4037] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving Out the Space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N ) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
M. Berkooz, R. Yacoby and A. Zait, Bounds on \( \mathcal{N} \) = 1 superconformal theories with global symmetries, JHEP 08 (2014) 008 [Erratum ibid. 01 (2015) 132] [arXiv:1402.6068] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Approaching the conformal window of O(n) × O(m) symmetric Landau-Ginzburg models using the conformal bootstrap, Phys. Rev. D 89 (2014) 126009 [arXiv:1404.0489] [INSPIRE].
F. Caracciolo, A. Castedo Echeverri, B. von Harling and M. Serone, Bounds on OPE Coefficients in 4D Conformal Field Theories, JHEP 10 (2014) 020 [arXiv:1406.7845] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Bootstrapping phase transitions in QCD and frustrated spin systems, Phys. Rev. D 91 (2015) 021901 [arXiv:1407.6195] [INSPIRE].
S.M. Chester, S.S. Pufu and R. Yacoby, Bootstrapping O(N ) vector models in 4 < d < 6, Phys. Rev. D 91 (2015) 086014 [arXiv:1412.7746] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Five dimensional O(N )-symmetric CFTs from conformal bootstrap, Phys. Lett. B 734 (2014) 193 [arXiv:1404.5201] [INSPIRE].
S.M. Chester, S. Giombi, L.V. Iliesiu, I.R. Klebanov, S.S. Pufu and R. Yacoby, Accidental Symmetries and the Conformal Bootstrap, JHEP 01 (2016) 110 [arXiv:1507.04424] [INSPIRE].
S.M. Chester, L.V. Iliesiu, S.S. Pufu and R. Yacoby, Bootstrapping O(N ) Vector Models with Four Supercharges in 3 ≤ d ≤ 4, JHEP 05 (2016) 103 [arXiv:1511.07552] [INSPIRE].
S.M. Chester and S.S. Pufu, Towards bootstrapping QED3 , JHEP 08 (2016) 019 [arXiv:1601.03476] [INSPIRE].
Y. Nakayama, Bootstrap bound for conformal multi-flavor QCD on lattice, JHEP 07 (2016) 038 [arXiv:1605.04052] [INSPIRE].
H. Iha, H. Makino and H. Suzuki, Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach, PTEP 2016 (2016) 053B03 [arXiv:1603.01995] [INSPIRE].
Y. Nakayama, Bootstrap experiments on higher dimensional CFTs, Int. J. Mod. Phys. A 33 (2018) 1850036 [arXiv:1705.02744] [INSPIRE].
J. Rong and N. Su, Scalar CFTs and Their Large N Limits, JHEP 09 (2018) 103 [arXiv:1712.00985] [INSPIRE].
S.M. Chester, L.V. Iliesiu, M. Mezei and S.S. Pufu, Monopole Operators in U(1) Chern-Simons-Matter Theories, JHEP 05 (2018) 157 [arXiv:1710.00654] [INSPIRE].
A. Stergiou, Bootstrapping hypercubic and hypertetrahedral theories in three dimensions, JHEP 05 (2018) 035 [arXiv:1801.07127] [INSPIRE].
Z. Li, Solving QED3 with Conformal Bootstrap, arXiv:1812.09281 [INSPIRE].
J. Rong and N. Su, Bootstrapping the \( \mathcal{N} \) = 1 Wess-Zumino models in three dimensions, arXiv:1910.08578 [INSPIRE].
S. Rychkov, Conformal Bootstrap in Three Dimensions?, arXiv:1111.2115 [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].
D. Gaiotto, D. Mazac and M.F. Paulos, Bootstrapping the 3d Ising twist defect, JHEP 03 (2014) 100 [arXiv:1310.5078] [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].
C.-M. Chang, M. Fluder, Y.-H. Lin and Y. Wang, Spheres, Charges, Instantons and Bootstrap: A Five-Dimensional Odyssey, JHEP 03 (2018) 123 [arXiv:1710.08418] [INSPIRE].
Z. Li and N. Su, 3D CFT Archipelago from Single Correlator Bootstrap, Phys. Lett. B 797 (2019) 134920 [arXiv:1706.06960] [INSPIRE].
C. Hasegawa and Y. Nakayama, Three ways to solve critical ϕ4 theory on 4 − ϵ dimensional real projective space: perturbation, bootstrap and Schwinger-Dyson equation, Int. J. Mod. Phys. A 33 (2018) 1850049 [arXiv:1801.09107] [INSPIRE].
C.N. Gowdigere, J. Santara and Sumedha, Conformal Bootstrap Signatures of the Tricritical Ising Universality Class, arXiv:1811.11442 [INSPIRE].
A. Stergiou, Bootstrapping MN and Tetragonal CFTs in Three Dimensions, SciPost Phys. 7 (2019) 010 [arXiv:1904.00017] [INSPIRE].
D. Poland and D. Simmons-Duffin, Bounds on 4D Conformal and Superconformal Field Theories, JHEP 05 (2011) 017 [arXiv:1009.2087] [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].
L.F. Alday and A. Bissi, The superconformal bootstrap for structure constants, JHEP 09 (2014) 144 [arXiv:1310.3757] [INSPIRE].
L.F. Alday and A. Bissi, Generalized bootstrap equations for \( \mathcal{N} \) = 4 SCFT, JHEP 02 (2015) 101 [arXiv:1404.5864] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, The \( \mathcal{N} \) = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [arXiv:1406.4814] [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].
N. Bobev, S. El-Showk, D. Mazac and M.F. Paulos, Bootstrapping SCFTs with Four Supercharges, JHEP 08 (2015) 142 [arXiv:1503.02081] [INSPIRE].
C. Beem, M. Lemos, L. Rastelli and B.C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D 93 (2016) 025016 [arXiv:1507.05637] [INSPIRE].
D. Poland and A. Stergiou, Exploring the Minimal 4D \( \mathcal{N} \) = 1 SCFT, JHEP 12 (2015) 121 [arXiv:1509.06368] [INSPIRE].
M. Lemos and P. Liendo, Bootstrapping \( \mathcal{N} \) = 2 chiral correlators, JHEP 01 (2016) 025 [arXiv:1510.03866] [INSPIRE].
Y.-H. Lin, S.-H. Shao, D. Simmons-Duffin, Y. Wang and X. Yin, \( \mathcal{N} \) = 4 superconformal bootstrap of the K 3 CFT, JHEP 05 (2017) 126 [arXiv:1511.04065] [INSPIRE].
Y.-H. Lin, S.-H. Shao, Y. Wang and X. Yin, (2, 2) superconformal bootstrap in two dimensions, JHEP 05 (2017) 112 [arXiv:1610.05371] [INSPIRE].
J.-B. Bae, D. Gang and J. Lee, 3d \( \mathcal{N} \) = 2 minimal SCFTs from Wrapped M5-branes, JHEP 08 (2017) 118 [arXiv:1610.09259] [INSPIRE].
M. Lemos, P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping \( \mathcal{N} \) = 3 superconformal theories, JHEP 04 (2017) 032 [arXiv:1612.01536] [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].
M. Cornagliotto, M. Lemos and V. Schomerus, Long Multiplet Bootstrap, JHEP 10 (2017) 119 [arXiv:1702.05101] [INSPIRE].
C.-M. Chang and Y.-H. Lin, Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions), JHEP 08 (2017) 128 [arXiv:1705.05392] [INSPIRE].
M. Cornagliotto, M. Lemos and P. Liendo, Bootstrapping the (A1 , A2 ) Argyres-Douglas theory, JHEP 03 (2018) 033 [arXiv:1711.00016] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 [arXiv:1711.07343] [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].
P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].
A. Atanasov, A. Hillman and D. Poland, Bootstrapping the Minimal 3D SCFT, JHEP 11 (2018) 140 [arXiv:1807.05702] [INSPIRE].
C.-M. Chang, M. Fluder, Y.-H. Lin, S.-H. Shao and Y. Wang, 3d N = 4 Bootstrap and Mirror Symmetry, arXiv:1910.03600 [INSPIRE].
R. Rattazzi, S. Rychkov and A. Vichi, Central Charge Bounds in 4D Conformal Field Theory, Phys. Rev. D 83 (2011) 046011 [arXiv:1009.2725] [INSPIRE].
F. Caracciolo and V.S. Rychkov, Rigorous Limits on the Interaction Strength in Quantum Field Theory, Phys. Rev. D 81 (2010) 085037 [arXiv:0912.2726] [INSPIRE].
P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFTd , JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].
S. El-Showk and M.F. Paulos, Bootstrapping Conformal Field Theories with the Extremal Functional Method, Phys. Rev. Lett. 111 (2013) 241601 [arXiv:1211.2810] [INSPIRE].
Y. Nakayama, Bootstrapping critical Ising model on three-dimensional real projective space, Phys. Rev. Lett. 116 (2016) 141602 [arXiv:1601.06851] [INSPIRE].
A. Castedo Echeverri, B. von Harling and M. Serone, The Effective Bootstrap, JHEP 09 (2016) 097 [arXiv:1606.02771] [INSPIRE].
A. Cappelli, L. Maffi and S. Okuda, Critical Ising Model in Varying Dimension by Conformal Bootstrap, JHEP 01 (2019) 161 [arXiv:1811.07751] [INSPIRE].
D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [INSPIRE].
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB, arXiv:1909.09745 [INSPIRE].
M. Go and Y. Tachikawa, autoboot: A generator of bootstrap equations with global symmetry, JHEP 06 (2019) 084 [arXiv:1903.10522] [INSPIRE].
J.A. Lipa, J.A. Nissen, D.A. Stricker, D.R. Swanson and T.C.P. Chui, Specific heat of liquid helium in zero gravity very near the lambda point, Phys. Rev. B 68 (2003) 174518 [cond-mat/0310163] [INSPIRE].
M. Hasenbusch, Monte Carlo study of an improved clock model in three dimensions, Phys. Rev. B 100 (2019) 224517 [arXiv:1910.05916] [INSPIRE].
M. Hasenbusch and E. Vicari, Anisotropic perturbations in three-dimensional O(N )-symmetric vector models, Phys. Rev. B 84 (2011) 125136.
D. Tilley and J. Tilley, Superfluidity and Superconductivity, Graduate Student Series in Physics, Taylor & Francis (1990).
M.R. Moldover, J.V. Sengers, R.W. Gammon and R.J. Hocken, Gravity effects in fluids near the gas-liquid critical point, Rev. Mod. Phys. 51 (1979) 79 [INSPIRE].
J.A. Lipa, D.R. Swanson, J.A. Nissen, T.C.P. Chui and U.E. Israelsson, Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point, Phys. Rev. Lett. 76 (1996) 944 [INSPIRE].
J.A. Lipa et al., Specific Heat of Helium Confined to a 57- mum Planar Geometry near the Lambda Point, Phys. Rev. Lett. 84 (2000) 4894 [INSPIRE].
A. Pelissetto and E. Vicari, Critical phenomena and renormalization group theory, Phys. Rept. 368 (2002) 549 [cond-mat/0012164] [INSPIRE].
E. Burovski, J. Machta, N. Prokof ’ev and B. Svistunov, High-precision measurement of the thermal exponent for the three-dimensionalxyuniversality class, Phys. Rev. B 74 (2006) .
A.I. Sokolov and M.A. Nikitina, Critical Exponents of Superfluid Helium and Pseudo-ϵ Expansion, Physica A 444 (2016) 177 [arXiv:1402.4318] [INSPIRE].
W. Xu, Y. Sun, J.-P. Lv and Y. Deng, High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class, Phys. Rev. B 100 (2019) 064525 [arXiv:1908.10990] [INSPIRE].
M. Campostrini, M. Hasenbusch, A. Pelissetto and E. Vicari, The Critical exponents of the superfluid transition in He-4, Phys. Rev. B 74 (2006) 144506 [cond-mat/0605083] [INSPIRE].
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT, JHEP 03 (2017) 086 [arXiv:1612.08471] [INSPIRE].
S. Albayrak, D. Meltzer and D. Poland, More Analytic Bootstrap: Nonperturbative Effects and Fermions, JHEP 08 (2019) 040 [arXiv:1904.00032] [INSPIRE].
R. Guida and J. Zinn-Justin, Critical exponents of the N vector model, J. Phys. A 31 (1998) 8103 [cond-mat/9803240] [INSPIRE].
F. Jasch and H. Kleinert, Fast-convergent resummation algorithm and critical exponents of ϕ4 theory in three dimensions, J. Math. Phys. 42 (2001) 52 [cond-mat/9906246] [INSPIRE].
S. Rychkov and Z.M. Tan, The E-expansion from conformal field theory, J. Phys. A 48 (2015) 29FT01 [arXiv:1505.00963] [INSPIRE].
P. Calabrese, A. Pelissetto and E. Vicari, Multicritical phenomena in O(n1 ) ⊕ O(n2 ) symmetric theories, Phys. Rev. B 67 (2003) 054505 [cond-mat/0209580] [INSPIRE].
M. De Prato, A. Pelissetto and E. Vicari, Third harmonic exponent in three-dimensional N vector models, Phys. Rev. B 68 (2003) 092403 [cond-mat/0302145] [INSPIRE].
M. Caselle and M. Hasenbusch, The Stability of the O(N ) invariant fixed point in three-dimensions, J. Phys. A 31 (1998) 4603 [cond-mat/9711080] [INSPIRE].
J.M. Carmona, A. Pelissetto and E. Vicari, The N component Ginzburg-Landau Hamiltonian with cubic anisotropy: A Six loop study, Phys. Rev. B 61 (2000) 15136 [cond-mat/9912115] [INSPIRE].
H. Shao, W. Guo and A.W. Sandvik, Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models, Phys. Rev. Lett. 124 (2020) 080602 [arXiv:1905.13640] [INSPIRE].
O. Nachtmann, Positivity constraints for anomalous dimensions, Nucl. Phys. B 63 (1973) 237 [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [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].
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].
D. Meltzer, Higher Spin ANEC and the Space of CFTs, JHEP 07 (2019) 001 [arXiv:1811.01913] [INSPIRE].
S. Rychkov unpublished work.
J.H. Park and S. Boyd, General heuristics for nonconvex quadratically constrained quadratic programming, arXiv:1703.07870.
C. Sun and R. Dai, An iterative rank penalty method for nonconvex quadratically constrained quadratic programs, SIAM J. Control Optim. 57 (2019) 3749.
C.B. Barber, D.P. Dobkin and H. Huhdanpaa, The quickhull algorithm for convex hulls, ACM Trans. Math. Software 22 (1996) 469.
P. Calabrese and P. Parruccini, Harmonic crossover exponents in O(n) models with the pseudo-E-expansion approach, Phys. Rev. B 71 (2005) 064416 [cond-mat/0411027] [INSPIRE].
E. Katz, S. Sachdev, E.S. Sørensen and W. Witczak-Krempa, Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo and holography, Phys. Rev. B 90 (2014) 245109 [arXiv:1409.3841] [INSPIRE].
L. Iliesiu, M. Koloğlu, R. Mahajan, E. Perlmutter and D. Simmons-Duffin, The Conformal Bootstrap at Finite Temperature, JHEP 10 (2018) 070 [arXiv:1802.10266] [INSPIRE].
J. Towns et al., Xsede: Accelerating scientific discovery, Comput. Sci. Eng. 16 (2014) 62.
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Chester, S.M., Landry, W., Liu, J. et al. Carving out OPE space and precise O(2) model critical exponents. J. High Energ. Phys. 2020, 142 (2020). https://doi.org/10.1007/JHEP06(2020)142
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DOI: https://doi.org/10.1007/JHEP06(2020)142