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Operator Dimensions from Moduli

Hellerman, Simeon and Maeda, Shunsuke and Watanabe, Masataka (2017) Operator Dimensions from Moduli. Journal of High Energy Physics, 2017 (10). Art. No. 089. ISSN 1126-6708. doi:10.1007/JHEP10(2017)089.

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We consider the operator spectrum of a three-dimensional N=2 superconformal field theory with a moduli space of one complex dimension, such as the fixed point theory with three chiral superfields X, Y, Z and a superpotential W = XYZ. By using the existence of an effective theory on each branch of moduli space, we calculate the anomalous dimensions of certain low-lying operators carrying large R-charge J. While the lowest primary operator is a BPS scalar primary, the second-lowest scalar primary is in a semi-short representation, with dimension exactly J + 1, a fact that cannot be seen directly from the XYZ Lagrangian. The third-lowest scalar primary lies in along multiplet with dimension J + 2−c_(−3) J^(−3) + O(J^(−4)), where c_(−3) is an unknown positive coefficient. The coefficient c_(−3) is proportional to the leading superconformal interaction term in the effective theory on moduli space. The positivity of c_(−3) does not follow from supersymmetry, but rather from unitarity of moduli scattering and the absence of superluminal signal propagation in the effective dynamics of the complex modulus. We also prove a general lemma, that scalar semi-short representations form a module over the chiral ring in a natural way, by ordinary multiplication of local operators. Combined with the existence of scalar semi-short states at large J, this proves the existence of scalar semi-short states at all values of J. Thus the combination of N=2 superconformal symmetry with the large-J expansion is more powerful than the sum of its parts.

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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. Received: June 27, 2017; Accepted: August 14, 2017; Published: October 12, 2017. The authors are deeply grateful to Thomas Dumitrescu, Daniel Jafferis, and Markus Luty for valuable discussions. 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 and MW acknowledge the support by JSPS Research Fellowship for Young Scientists. SH is grateful to the Harvard Center for the Fundamental Laws of Nature, the Burke Institute at Caltech, and the Galileo Galilei Institute during the “Conformal Field Theories and Renormalization Group Flows in Dimensions d > 2” conference, for hospitality while this work was in progress. Some of the calculations of this work were done with the help of the excellent MathematicaTM package diffgeo.m developed by M. Headrick [38].
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, Effective Field Theories, Extended Supersymmetry, Supersymmetric Effective Theories
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Issue or Number:10
Record Number:CaltechAUTHORS:20170630-094747476
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Official Citation:Hellerman, S., Maeda, S. & Watanabe, M. J. High Energ. Phys. (2017) 2017: 89.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78720
Deposited By: Joy Painter
Deposited On:30 Jun 2017 17:01
Last Modified:15 Nov 2021 17:42

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