Abstract
We apply the OPE inversion formula on thermal two-point functions of fermions to obtain thermal one-point function of fermion bi-linears appearing in the corresponding OPE. We primarily focus on the OPE channel which contains the stress tensor of the theory. We apply our formalism to the mean field theory of fermions and verify that the inversion formula reproduces the spectrum as well as their corresponding thermal one-point functions. We then examine the large N critical Gross-Neveu model in d = 2k + 1 dimensions with k even and at finite temperature. We show that stress tensor evaluated from the inversion formula agrees with that evaluated from the partition function at the critical point. We demonstrate the expectation values of 3 different classes of higher spin currents are all related to each other by numerical constants, spin and the thermal mass. We evaluate the ratio of the thermal expectation values of higher spin currents at the critical point to the Gaussian fixed point or the Stefan-Boltzmann result, both for the large N critical O(N) model and the Gross-Neveu model in odd dimensions. This ratio is always less than one and it approaches unity on increasing the spin with the dimension d held fixed. The ratio however approaches zero when the dimension d is increased with the spin held fixed.
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References
L. Iliesiu et al., The Conformal Bootstrap at Finite Temperature, JHEP 10 (2018) 070 [arXiv:1802.10266] [INSPIRE].
A.C. Petkou and A. Stergiou, Dynamics of Finite-Temperature Conformal Field Theories from Operator Product Expansion Inversion Formulas, Phys. Rev. Lett. 121 (2018) 071602 [arXiv:1806.02340] [INSPIRE].
L. Iliesiu, M. Koloğlu and D. Simmons-Duffin, Bootstrapping the 3d Ising model at finite temperature, JHEP 12 (2019) 072 [arXiv:1811.05451] [INSPIRE].
Y. Gobeil, A. Maloney, G.S. Ng and J.-Q. Wu, Thermal Conformal Blocks, SciPost Phys. 7 (2019) 015 [arXiv:1802.10537] [INSPIRE].
C. Luo and Y. Wang, Casimir energy and modularity in higher-dimensional conformal field theories, JHEP 07 (2023) 028 [arXiv:2212.14866] [INSPIRE].
N. Benjamin, J. Lee, H. Ooguri and D. Simmons-Duffin, Universal Asymptotics for High Energy CFT Data, arXiv:2306.08031 [INSPIRE].
E. Marchetto, A. Miscioscia and E. Pomoni, Broken (super) conformal Ward identities at finite temperature, arXiv:2306.12417 [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].
A. Stergiou, Symplectic critical models in 6 + ϵ dimensions, Phys. Lett. B 751 (2015) 184 [arXiv:1508.03639] [INSPIRE].
H. Osborn and A. Stergiou, CT for non-unitary CFTs in higher dimensions, JHEP 06 (2016) 079 [arXiv:1603.07307] [INSPIRE].
F. Gliozzi, A. Guerrieri, A.C. Petkou and C. Wen, Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion, Phys. Rev. Lett. 118 (2017) 061601 [arXiv:1611.10344] [INSPIRE].
F. Gliozzi, A.L. Guerrieri, A.C. Petkou and C. Wen, The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points, JHEP 04 (2017) 056 [arXiv:1702.03938] [INSPIRE].
A. Gadde and T. Sharma, Constraining conformal theories in large dimensions, JHEP 02 (2022) 035 [arXiv:2002.10147] [INSPIRE].
A. Gadde, M. Jagadale, S. Jain and T. Sharma, Bound on the central charge of CFTs in large dimension, JHEP 05 (2023) 146 [arXiv:2301.04980] [INSPIRE].
E.G. Filothodoros, A.C. Petkou and N.D. Vlachos, The fermion-boson map for large d, Nucl. Phys. B 941 (2019) 195 [arXiv:1803.05950] [INSPIRE].
E.G. Filothodoros, Strongly coupled fermions in odd dimensions and the running cut-off Λd, arXiv:2306.14652 [INSPIRE].
S. Giombi et al., The O(N) Model in 4 < d < 6: Instantons and complex CFTs, Phys. Rev. D 101 (2020) 045013 [arXiv:1910.02462] [INSPIRE].
M. Moshe and J. Zinn-Justin, Quantum field theory in the large N limit: A Review, Phys. Rept. 385 (2003) 69 [hep-th/0306133] [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 [INSPIRE].
K. Lang and W. Ruhl, The Critical O(N) σ-model at dimensions 2 < d < 4: Fusion coefficients and anomalous dimensions, Nucl. Phys. B 400 (1993) 597 [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.C. Petkou, CT and CJ up to next-to-leading order in 1/N in the conformally invariant O(N) vector model for 2 < d < 4, Phys. Lett. B 359 (1995) 101 [hep-th/9506116] [INSPIRE].
S. Giombi et al., 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].
S. Jain, S.P. Trivedi, S.R. Wadia and S. Yokoyama, Supersymmetric Chern-Simons Theories with Vector Matter, JHEP 10 (2012) 194 [arXiv:1207.4750] [INSPIRE].
O. Aharony et al., The Thermal Free Energy in Large N Chern-Simons-Matter Theories, JHEP 03 (2013) 121 [arXiv:1211.4843] [INSPIRE].
G. Gur-Ari, S.A. Hartnoll and R. Mahajan, Transport in Chern-Simons-Matter Theories, JHEP 07 (2016) 090 [arXiv:1605.01122] [INSPIRE].
S. Ghosh and S. Mazumdar, Thermal correlators and bosonization dualities in large N Chern-Simons matter theories, JHEP 02 (2023) 042 [arXiv:1912.06589] [INSPIRE].
A. Mishra, On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter, JHEP 01 (2021) 109 [arXiv:2010.03699] [INSPIRE].
M. Grinberg and J. Maldacena, Proper time to the black hole singularity from thermal one-point functions, JHEP 03 (2021) 131 [arXiv:2011.01004] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Correlation functions in finite temperature CFT and black hole singularities, JHEP 06 (2021) 048 [arXiv:2102.11891] [INSPIRE].
B. McInnes, The special role of toroidal black holes in holography, Nucl. Phys. B 989 (2023) 116126 [arXiv:2206.00198] [INSPIRE].
G. Georgiou and D. Zoakos, Holographic correlation functions at finite density and/or finite temperature, JHEP 11 (2022) 087 [arXiv:2209.14661] [INSPIRE].
D. Berenstein and R. Mancilla, Aspects of thermal one-point functions and response functions in AdS black holes, Phys. Rev. D 107 (2023) 126010 [arXiv:2211.05144] [INSPIRE].
J.R. David and S. Kumar, Thermal one point functions, large d and interior geometry of black holes, JHEP 03 (2023) 256 [arXiv:2212.07758] [INSPIRE].
M. Dodelson et al., Holographic thermal correlators from supersymmetric instantons, SciPost Phys. 14 (2023) 116 [arXiv:2206.07720] [INSPIRE].
A. Bhatta and T. Mandal, Exact thermal correlators of holographic CFTs, JHEP 02 (2023) 222 [arXiv:2211.02449] [INSPIRE].
M. Dodelson, C. Iossa, R. Karlsson and A. Zhiboedov, A thermal product formula, arXiv:2304.12339 [INSPIRE].
E. Parisini, K. Skenderis and B. Withers, Embedding formalism for CFTs in general states on curved backgrounds, Phys. Rev. D 107 (2023) 066022 [arXiv:2209.09250] [INSPIRE].
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David, J.R., Kumar, S. Thermal one-point functions: CFT’s with fermions, large d and large spin. J. High Energ. Phys. 2023, 143 (2023). https://doi.org/10.1007/JHEP10(2023)143
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DOI: https://doi.org/10.1007/JHEP10(2023)143