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Bosonic tensor models at large N and small ϵ

Author(s): Giombi, Simone; Klebanov, Igor R; Tarnopolsky, Grigory

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Abstract: We study the spectrum of the large N quantum field theory of bosonic rank-3 tensors, the quartic interactions of which are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to determine the scaling dimensions of the bilinear operators of arbitrary spin. Using the fact that the theory is renormalizable in d ¼ 4, we compare some of these results with the 4 − ϵ expansion, finding perfect agreement. This helps elucidate why the dimension of operator ϕabcϕabc is complex for d < 4: the large N fixed point in d ¼ 4 − ϵ has complex values of the couplings for some of the OðNÞ3 invariant operators. We show that a similar phenomenon holds in the OðNÞ2 symmetric theory of a matrix field ϕab, where the double-trace operator has a complex coupling in 4 − ϵ dimensions. We also study the spectra of bosonic theories of rank-q − 1 tensors with ϕq interactions. In dimensions d > 1.93, there is a critical value of q, above which we have not found any complex scaling dimensions. The critical value is a decreasing function of d, and it becomes 6 in d ≈ 2.97. This raises a possibility that the large N theory of rank-5 tensors with sextic potential has an IR fixed point which is free of perturbative instabilities for 2.97 < d < 3. This theory may be studied using renormalized perturbation theory in d ¼ 3 − ϵ.
Publication Date: 21-Nov-2017
Electronic Publication Date: 21-Nov-2017
Citation: Giombi, Simone, Klebanov, Igor R, Tarnopolsky, Grigory. (Bosonic tensor models at large <mml:math xmlns:mml="" display="inline"><mml:mi>N</mml:mi></mml:math> and small <mml:math xmlns:mml="" display="inline"><mml:mi>ε</mml:mi></mml:math>. Physical Review D, 96 (10), 10.1103/physrevd.96.106014
DOI: doi:10.1103/physrevd.96.106014
ISSN: 2470-0010
EISSN: 2470-0029
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review D
Version: Author's manuscript

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