Prismatic large models for bosonic tensors
We study the O(N)3 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 O(N)3 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 = 1 model where our approach gives a slightly negative scaling dimension for Φ, while the spectrum of bilinear operators is free of complex dimensions.
- Research Organization:
- Harvard Univ., Cambridge, MA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- Grant/Contract Number:
- de-sc0007870; SC0007870; PHY-1620542
- OSTI ID:
- 1482146
- Alternate ID(s):
- OSTI ID: 1610981
- Journal Information:
- Physical Review D, Journal Name: Physical Review D Vol. 98 Journal Issue: 10; ISSN 2470-0010
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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