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On the Large R-charge Expansion in N=2 Superconformal Field Theories

Hellerman, Simeon and Maeda, Shunsuke (2017) On the Large R-charge Expansion in N=2 Superconformal Field Theories. Journal of High Energy Physics, 2017 (12). Art. No. 135. ISSN 1126-6708. doi:10.1007/JHEP12(2017)135.

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In this note we study two point functions of Coulomb branch chiral ring elements with large R-charge, in quantum field theories with N = 2 superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of [1], to estimate the two-point correlation function Yn ≡ |x − y|2n∆O(O(x))n(O¯(y))n�in the limit where the operator insertion On has large total R-charge J = n∆O. We show that Yn has a nontrivial but universal asymptotic expansion at large J , of the form Yn = J !�|NO|2π�2JJα Y˜n ,where Y˜ n approaches a constant as n → ∞, and NO is an n-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent α is a positive number proportional to the difference between the a-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions for the logarithm Bn = log(Yn), up to and including order log(J ) against exact results from supersymmetric localization [2–5]. In the case of N = 4 we find precise agreement and in the case N = 2 we find reasonably good numerical agreement at J ' 60 using the no-instanton approximation to the S 4 partition function. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of [6–9]. In this way, we show the large-R-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua.

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Additional Information:© 2017 The Author(s). 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. Article funded by SCOAP3. Received: October 31, 2017; Accepted: December 5, 2017; Published: December 27, 2017. The authors note helpful discussions with Philip Argyres, Nozomu Kobayashi, Markus Luty, Mauricio Romo, Vyacheslav Rychkov, Masataka Watanabe, and Alexander Zhiboedov. We thank Zohar Komargodski and Kyriakos Papadodimas for reading the manuscript and for valuable comments. We are particularly grateful to Daniel Jafferis for early discussions on the relationship between the large R-charge limit and the dynamics of moduli space, as well as bringing refs. [2–5] to our attention as a possible check on the large-J expansion beyond the free-field approximation. The work of SH is supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan; by the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers; and also supported in part by JSPS KAKENHI Grant Numbers JP22740153, JP26400242. SM acknowledges the support by JSPS Research Fellowship for Young Scientists. SH also thanks the Walter Burke Institute for Theoretical Physics at Caltech, the Stanford Institute for Theoretical Physics, and the Harvard Center for the Fundamental Laws of Nature, for hospitality while this work was in progress.
Group:Walter Burke Institute for Theoretical Physics
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Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)JP22740153
Japan Society for the Promotion of Science (JSPS)JP26400242
Subject Keywords:Conformal Field Theory; Anomalies in Field and String Theories; Extended Supersymmetry; Supersymmetric Effective Theories
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Issue or Number:12
Record Number:CaltechAUTHORS:20171028-162312414
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Official Citation:Hellerman, S. & Maeda, S. J. High Energ. Phys. (2017) 2017: 135.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82761
Deposited By: Joy Painter
Deposited On:29 Oct 2017 01:52
Last Modified:15 Nov 2021 19:52

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