HOME ::
SCOAP^{3} ::
HELP ::
ABOUT ::
IDEA BOARD |

Home > Physical Review D (APS) > Prismatic large <math><mi>N</mi></math> 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 ${\varphi}^{abc}$ 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-\epsilon $ 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 $\epsilon $ expansions of various operator dimensions agrees with the Schwinger-Dyson equations. Furthermore, the $\epsilon $ expansion allows us to calculate the $1/N$ corrections to operator dimensions. The prismatic fixed point in $3-\epsilon $ dimensions survives down to $N\approx 53.65$, 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 $\varphi $, 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