Prismatic large N models for bosonic tensors

Giombi, Simone (Department of Physics, Princeton University, Princeton, New Jersey 08544, USA) ; Klebanov, Igor R. (Department of Physics, Princeton University, Princeton, New Jersey 08544, USA) (Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA) ; Popov, Fedor (Department of Physics, Princeton University, Princeton, New Jersey 08544, USA) ; Prakash, Shiroman (Department of Physics and Computer Science, Dayalbagh Educational Institute, Agra 282005, India) ; Tarnopolsky, Grigory (Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA)

14 November 2018

Abstract: 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 3ε 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 3ε dimensions survives down to N53.65, 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.


Published in: Physical Review D 98 (2018)
Published by: APS
DOI: 10.1103/PhysRevD.98.105005
arXiv: 1808.04344
License: CC-BY-4.0



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