TY - JOUR

T1 - Bosonic tensor models at large N and small ϵ

AU - Giombi, Simone

AU - Klebanov, Igor R.

AU - Tarnopolsky, Grigory

N1 - Funding Information:
We thank S. Chester, V. Kirilin, F. Popov, D. Stanford, and E. Witten for very useful discussions. The work of S. G. was supported in part by the U.S. NSF under Grant No. PHY-1620542. The work of I. R. K. and G. T. was supported in part by the U.S. NSF under Grant No. PHY-1620059. G. T. also acknowledges the support of a Myhrvold-Havranek Innovative Thinking Fellowship.
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017

Y1 - 2017

N2 - 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=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=4-ϵ has complex values of the couplings for some of the O(N)3 invariant operators. We show that a similar phenomenon holds in the O(N)2 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

AB - 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=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=4-ϵ has complex values of the couplings for some of the O(N)3 invariant operators. We show that a similar phenomenon holds in the O(N)2 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

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U2 - 10.1103/PhysRevD.96.106014

DO - 10.1103/PhysRevD.96.106014

M3 - Article

AN - SCOPUS:85037153995

SN - 2470-0010

VL - 96

JO - Physical Review D

JF - Physical Review D

IS - 10

M1 - 106014

ER -