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Prismatic large N models for bosonic tensors

Author(s): Giombi, Simone; Klebanov, Igor R; Popov, Fedor; Prakash, Shiroman; Tarnopolsky, Grigory

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Abstract: We study the OðNÞ3 symmetric quantum field theory of a bosonic tensor ϕabc with sextic interactions. Its large N limit is dominated by a positive-definite operator, whose index structure has the topology of a prism. We present a large N solution of the model using Schwinger-Dyson equations to sum the leading diagrams, finding that for 2.81 < d < 3 and for d < 1.68 the spectrum of bilinear operators has no complex scaling dimensions. We also develop perturbation theory in 3 − ϵ dimensions including eight OðNÞ3 invariant operators necessary for the renormalizability. For sufficiently large N, we find a “prismatic” fixed point of the renormalization group, where all eight coupling constants are real. The large N limit of the resulting ϵ expansions of various operator dimensions agrees with the Schwinger- Dyson equations. Furthermore, the ϵ expansion allows us to calculate the 1=N corrections to operator dimensions. The prismatic fixed point in 3 − ϵ dimensions survives down to N ≈ 53.65, where it merges with another fixed point and becomes complex. We also discuss the d ¼ 1 model where our approach gives a slightly negative scaling dimension for ϕ, while the spectrum of bilinear operators is free of complex dimensions.
Publication Date: 14-Nov-2018
Electronic Publication Date: 14-Nov-2018
Citation: Giombi, Simone, Klebanov, Igor R, Popov, Fedor, Prakash, Shiroman, Tarnopolsky, Grigory. (Prismatic large <mml:math xmlns:mml="" display="inline"><mml:mi>N</mml:mi></mml:math> models for bosonic tensors. Physical Review D, 98 (10), 10.1103/physrevd.98.105005
DOI: doi:10.1103/physrevd.98.105005
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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