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Title: On the large charge sector in the critical O(N) model at large N
A bstract We study operators in the rank- j totally symmetric representation of O ( N ) in the critical O ( N ) model in arbitrary dimension d , in the limit of large N and large charge j with j/N ≡ $$ \hat{j} $$ j ̂ fixed. The scaling dimensions of the operators in this limit may be obtained by a semiclassical saddle point calculation. Using the standard Hubbard-Stratonovich description of the critical O ( N ) model at large N , we solve the relevant saddle point equation and determine the scaling dimensions as a function of d and $$ \hat{j} $$ j ̂ , finding agreement with all existing results in various limits. In 4 < d < 6, we observe that the scaling dimension of the large charge operators becomes complex above a critical value of the ratio j/N , signaling an instability of the theory in that range of d . Finally, we also derive results for the correlation functions involving two “heavy” and one or two “light” operators. In particular, we determine the form of the “heavy-heavy-light” OPE coefficients as a function of the charges and d .  more » « less
Award ID(s):
1914860
NSF-PAR ID:
10380979
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2021
Issue:
9
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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