Abstract
Using supersymmetric localization, we study the sector of chiral primary operators (Tr ϕ2)n with large R-charge 4n in \( \mathcal{N} \) = 2 four-dimensional superconformal theories in the weak coupling regime g → 0, where λ ≡ g2n is kept fixed as n → ∞, g representing the gauge theory coupling(s). In this limit, correlation functions G2n of these operators behave in a simple way, with an asymptotic behavior of the form \( {G}_{2n}\approx {F}_{\infty}\left(\uplambda \right){\left(\frac{\uplambda}{2\pi e}\right)}^{2n} \) nα, modulo O(1/n) corrections, with \( \alpha =\frac{1}{2} \dim \left(\mathfrak{g}\right) \) for a gauge algebra \( \mathfrak{g} \) and a universal function F∞(λ). As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in \( \mathcal{N}=2\kern0.5em \mathfrak{s}\mathfrak{u}(N) \) gauge theory with 2N fundamental hypermultiplets.
Article PDF
Similar content being viewed by others
References
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super-Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [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].
L. Álvarez-Gaumé, O. Loukas, D. Orlando and S. Reffert, Compensating strong coupling with large charge, JHEP 04 (2017) 059 [arXiv:1610.04495] [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].
S. Hellerman and S. Maeda, On the large R-charge expansion in \( \mathcal{N} \) = 2 superconformal field theories, JHEP 12 (2017) 135 [arXiv:1710.07336] [INSPIRE].
O. Loukas, Abelian scalar theory at large global charge, Fortsch. Phys. 65 (2017) 1700028 [arXiv:1612.08985] [INSPIRE].
S. Hellerman, N. Kobayashi, S. Maeda and M. Watanabe, A note on inhomogeneous ground states at large global charge, arXiv:1705.05825 [INSPIRE].
D. Banerjee, S. Chandrasekharan and D. Orlando, Conformal dimensions via large charge expansion, Phys. Rev. Lett. 120 (2018) 061603 [arXiv:1707.00711] [INSPIRE].
O. Loukas, D. Orlando and S. Reffert, Matrix models at large charge, JHEP 10 (2017) 085 [arXiv:1707.00710] [INSPIRE].
S. Hellerman, S. Maeda and M. Watanabe, Operator dimensions from moduli, JHEP 10 (2017) 089 [arXiv:1706.05743] [INSPIRE].
D. Jafferis, B. Mukhametzhanov and A. Zhiboedov, Conformal bootstrap at large charge, arXiv:1710.11161 [INSPIRE].
G. Cuomo et al., Rotating superfluids and spinning charged operators in conformal field theory, Phys. Rev. D 97 (2018) 045012 [arXiv:1711.02108] [INSPIRE].
O. Loukas, A matrix CFT at multiple large charges, arXiv:1711.07990 [INSPIRE].
M. Lemos, P. Liendo, M. Meineri and S. Sarkar, Universality at large transverse spin in defect CFT, arXiv:1712.08185 [INSPIRE].
E. Gerchkovitz et al., Correlation functions of Coulomb branch operators, JHEP 01 (2017) 103 [arXiv:1602.05971] [INSPIRE].
K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, tt ∗ equations, localization and exact chiral rings in 4d \( \mathcal{N} \) = 2 SCFTs, JHEP 02 (2015) 122 [arXiv:1409.4212] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, On exact correlation functions in SU(N ) \( \mathcal{N} \) = 2 superconformal QCD, JHEP 11 (2015) 198 [arXiv:1508.03077] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Large N correlation functions in superconformal field theories, JHEP 06 (2016) 109 [arXiv:1604.07416] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Operator mixing in large N superconformal field theories on S 4 and correlators with Wilson loops, JHEP 12 (2016) 120 [arXiv:1607.07878] [INSPIRE].
M. Baggio, V. Niarchos, K. Papadodimas and G. Vos, Large-N correlation functions in \( \mathcal{N} \) = 2 superconformal QCD, JHEP 01 (2017) 101 [arXiv:1610.07612] [INSPIRE].
A. Pini, D. Rodriguez-Gomez and J.G. Russo, Large N correlation functions \( \mathcal{N} \) = 2 superconformal quivers, JHEP 08 (2017) 066 [arXiv:1701.02315] [INSPIRE].
M. Billó et al., Two-point correlators in N = 2 gauge theories, Nucl. Phys. B 926 (2018) 427 [arXiv:1705.02909] [INSPIRE].
M. Billó, F. Galvagno, P. Gregori and A. Lerda, Correlators between Wilson loop and chiral operators in \( \mathcal{N} \) = 2 conformal gauge theories, JHEP 03 (2018) 193 [arXiv:1802.09813] [INSPIRE].
J. Gomis et al., Anomalies, conformal manifolds and spheres, JHEP 03 (2016) 022 [arXiv:1509.08511] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, Exact correlation functions in SU(2) \( \mathcal{N} \) = 2 superconformal QCD, Phys. Rev. Lett. 113 (2014) 251601 [arXiv:1409.4217] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].
D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 [hep-th/9711035] [INSPIRE].
S. Corley and S. Ramgoolam, Finite factorization equations and sum rules for BPS correlators in N = 4 SYM theory, Nucl. Phys. B 641 (2002) 131 [hep-th/0205221] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1803.00580
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bourget, A., Rodriguez-Gomez, D. & Russo, J.G. A limit for large R-charge correlators in \( \mathcal{N} \) = 2 theories. J. High Energ. Phys. 2018, 74 (2018). https://doi.org/10.1007/JHEP05(2018)074
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2018)074