Abstract
We compute general higher-point functions in the sector of large charge operators ϕn,\( {\overline{\phi}}^n \) at large charge in O(2) \( {\left(\overline{\phi}\phi \right)}^2 \) theory. We find that there is a special class of “extremal” correlators having only one insertion of \( {\overline{\phi}}^n \) that have a remarkably simple form in the double-scaling limit n →∞ at fixed g n2 ≡ λ, where g ~ ϵ is the coupling at the O(2) Wilson-Fisher fixed point in 4 − ϵ dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for \( \left\langle \phi {\left({x}_1\right)}^n\phi {\left({x}_2\right)}^n\overline{\phi}{\left({x}_3\right)}^n\overline{\phi}{\left({x}_4\right)}^n\right\rangle \), which reveals an interesting structure.
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S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP12 (2015) 071 [arXiv:1505.01537] [INSPIRE].
L. Álvarez-Gaumé, O. Loukas, D. Orlando and S. Reffert, Compensating strong coupling with large charge, JHEP04 (2017) 059 [arXiv:1610 .04495] [INSPIRE].
A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data, JHEP06 (2017) 011 [arXiv:1611.02912] [INSPIRE].
G. Arias-Tamargo, D. Rodriguez-Gomez and J.G. Russo, The large charge limit of scalar field theories and the Wilson-Fisher fixed point at ϵ = 0, JHEP10 (2019) 201 [arXiv:1908.11347] [INSPIRE].
G. Badel, G. Cuomo, A. Monin and R. Rattazzi, The ϵ-expansion Meets Semiclassics, JHEP11 (2019) 110 [arXiv:1909.01269] [INSPIRE].
M. Watanabe, Accessing Large Global Charge via the ϵ-Expansion, arXiv:1909.01337 [INSPIRE].
G. Badel, G. Cuomo, A. Monin and R. Rattazzi, Feynma n diagrams and the large charge expansion in 3-𝜀 dimensions, Phys. Lett.B 802 (2020) 135202 [arXiv:1911.08505] [INSPIRE].
M.V. Libanov, V.A. Rubakov, D.T. Son and S.V. Troitsky, Exponentiation of multiparticle amplitudes in scalar theories, Phys. Rev.D 50 (1994) 7553 [hep-ph/9407381] [INSPIRE].
M.V. Libanov, D.T. Son and S.V. Troitsky, Exponentiation of multiparticle amplitudes in scalar theories. 2. Universality of the exponent, Phys. Rev.D 52 (1995) 3679 [hep-ph/9503412] [INSPIRE].
D.T. Son, Semiclassical approach for multiparticle production in scalar theories, Nucl. Phys.B 477 (1996) 378 [hep-ph/9505338] [INSPIRE].
A. Bourget , D. Rodriguez-Gomez and J.G. Russo, A limit for large R-charge correlators in \( \mathcal{N} \) = 2 theories, JHEP05 (2018) 074 [arXiv:1803.00580] [INSPIRE].
M. Beccaria, On the large R-charge \( \mathcal{N} \) = 2 chiral correlators and the Toda equation, JHEP02 (2019) 009 [arXiv:1809.06280] [INSPIRE].
M. Beccaria, Double scaling limit of N = 2 chiral correlators with Maldacena-Wilson loop, JHEP02 (2019) 095 [arXiv:1810.10483] [INSPIRE].
A. Grassi, Z. Komargodski and L. Tizzano, Extremal Correlators and Random Matrix Theory, arXiv:1908.10306 [INSPIRE].
D.Z. Freedman, K. Johnson and J.I. Latorre, Differential regularization and renormalization: A New method of calculation in quantum field theory, Nucl. Phys.B 371 (1992) 353 [INSPIRE].
F.A. Dolan and H. Osborn, Implications of N = 1 superconformal symmetry for chiral fields, Nucl. Phys.B 593 (2001) 599 [hep-th/0006098] [INSPIRE].
K. Symanzik, On Calculations in conformal invariant field theories, Lett. Nuovo Cim.3 (1972) 734 [INSPIRE].
A.I. Davydychev and J.B. Tausk, Two-loop self-energy diagrams with different masses and the momentum expansion, Nucl. Phys.B 397 (1993) 123 [INSPIRE].
N.I. Usyukina and A.I. Davydychev, An Approach to the evaluation of three and four point ladder diagrams, Phys. Lett.B 298 (1993) 363 [INSPIRE].
N.I. Usyukina and A.I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs, Phys. Lett.B 305 (1993) 136 [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys.B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
M. Cvitkovic, A.-S. Smith and J. Pande, Asymptotic expansions of the hypergeometric function with two large parameters — application to the partition function of a lattice gas in a field of traps, J. Phys.A 50 (2017) 265206 [arXiv:1602.05146 [INSPIRE].
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ArXiv ePrint: 1912.01623
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Arias-Tamargo, G., Rodriguez-Gomez, D. & Russo, J.G. Correlation functions in scalar field theory at large charge. J. High Energ. Phys. 2020, 171 (2020). https://doi.org/10.1007/JHEP01(2020)171
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DOI: https://doi.org/10.1007/JHEP01(2020)171