Abstract
In this paper, I calculate the large N limit of marginal O(N) models with non-polynomial potentials in arbitrary odd dimensions d. This results in a new class of interacting pure conformal field theories (CFTs) in d = 3 + 4n for any n ∈ ℤ+. Similarly, in d = 3 + 4n I calculate the thermal entropy for all couplings on R2+4n × S1 for n = 0, 1, 2, 3. In 2+1 dimensions I find the strong-to-weak coupling ratio of the thermal entropy to be 4/5, matching recent results, and further extend this analysis to higher odd dimensions. Next, I calculated the vacuum entanglement entropy \( {s}_{\textrm{EE}}^d \) on Sd−2 for all couplings in arbitrary odd d in the large N limit. I find the vacuum entanglement entropy on Sd−2 to be not only solvable but also constant for all couplings λ. Thus, in the large N limit, the vacuum entanglement entropy on Sd−2 for odd d is constant for all λ, in contrast to the thermal entropy which is shown to also be monotonically decreasing with λ in d = 3 + 4n.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
O. DeWolfe and P. Romatschke, Strong coupling universality at large N for pure CFT thermodynamics in 2 + 1 dimensions, JHEP 10 (2019) 272 [arXiv:1905.06355] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [hep-th/9805156] [INSPIRE].
P. Romatschke, Finite-temperature conformal field theory results for all couplings: O(N) model in 2 + 1 dimensions, Phys. Rev. Lett. 122 (2019) 231603 [Erratum ibid. 123 (2019) 209901] [arXiv:1904.09995] [INSPIRE].
M. Laine and A. Vuorinen, Basics of thermal field theory, Lect. Notes Phys. 925 (2016) 1701 [arXiv:1701.01554] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-theorem without supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
P. Romatschke, Shear Viscosity at Infinite Coupling: A Field Theory Calculation, Phys. Rev. Lett. 127 (2021) 111603 [arXiv:2104.06435] [INSPIRE].
M.B. Pinto, Three dimensional Yukawa models and CFTs at strong and weak couplings, Phys. Rev. D 102 (2020) 065005 [arXiv:2007.03784] [INSPIRE].
H. Liu and M. Mezei, A refinement of entanglement entropy and the number of degrees of freedom, JHEP 04 (2013) 162 [arXiv:1202.2070] [INSPIRE].
M. Mezei, Entanglement entropy across a deformed sphere, Phys. Rev. D 91 (2015) 045038 [arXiv:1411.7011] [INSPIRE].
J.P. Blaizot, E. Iancu, U. Kraemmer and A. Rebhan, Hard thermal loops and the entropy of supersymmetric Yang-Mills theories, JHEP 06 (2007) 035 [hep-ph/0611393] [INSPIRE].
A. Allais and M. Mezei, Some results on the shape dependence of entanglement and Rényi entropies, Phys. Rev. D 91 (2015) 046002 [arXiv:1407.7249] [INSPIRE].
N. Shimakura, Partial differential operators of elliptic type, American Mathematical Society (1992).
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].
S. Sachdev, Polylogarithm identities in a conformal field theory in three-dimensions, Phys. Lett. B 309 (1993) 285 [hep-th/9305131] [INSPIRE].
I.T. Drummond, R.R. Horgan, P.V. Landshoff and A. Rebhan, Foam diagram summation at finite temperature, Nucl. Phys. B 524 (1998) 579 [hep-ph/9708426] [INSPIRE].
S.W. Hawking, Zeta function regularization of path integrals in curved spacetime, in Euclidean Quantum Gravity, World Scientific (1992) pg. 114.
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Grable, S. Interacting CFTs for all couplings: thermal versus entanglement entropy at large N. J. High Energ. Phys. 2022, 133 (2022). https://doi.org/10.1007/JHEP10(2022)133
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DOI: https://doi.org/10.1007/JHEP10(2022)133