Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Large-$N$ limit of $O(N)^3$-invariant general sextic tensor model

Gaetan Bardy, Thomas Krajewski, Thomas Muller, Adrian Tanasa

TL;DR

This work extends the large-$N$ analysis to the $O(N)^3$-invariant sextic tensor model with all eight invariant bubbles, identifying the full set of dominant graphs in the $1/N$ expansion. By employing an adapted intermediate-field method (real and complex fields) and cyclotomic jacket analysis, the authors reduce sextic interactions to a quartic sector (tetrahedron and pillow) and demonstrate that wheel interactions cannot mix with other sextics in dominant graphs. They systematically classify dominant graphs for each interaction, uncover new mixed-bubble structures, and discover four fundamental dominant graphs that mix multiple interactions, all with vanishing degree. The results reveal a richer large-$N$ diagrammatics than in prior tensor models, including infinite families of dominant graphs, and set the stage for deeper renormalization and Schwinger-Dyson analyses in this broader invariant class.

Abstract

We study a sextic tensor model where the interaction terms are given by all $O(N)^3$-invariant bubbles. The class of invariants studied here is thus a larger one that the class of the $U(N)^3$-invariant sextic tensor model. We implement the large $N$ limit mechanism for this general model and we explicitly identify the dominant graphs in the $1/N$ expansion. This class of dominant graphs contains tadpole graphs, melonic graphs but also new types of tensor graphs. Our analysis adapts the tensorial intermediate field method, previously applied only to the prismatic interaction, to all connected sextic interactions except the wheel interaction, which we treat separately using a cycle analysis.

Large-$N$ limit of $O(N)^3$-invariant general sextic tensor model

TL;DR

This work extends the large- analysis to the -invariant sextic tensor model with all eight invariant bubbles, identifying the full set of dominant graphs in the expansion. By employing an adapted intermediate-field method (real and complex fields) and cyclotomic jacket analysis, the authors reduce sextic interactions to a quartic sector (tetrahedron and pillow) and demonstrate that wheel interactions cannot mix with other sextics in dominant graphs. They systematically classify dominant graphs for each interaction, uncover new mixed-bubble structures, and discover four fundamental dominant graphs that mix multiple interactions, all with vanishing degree. The results reveal a richer large- diagrammatics than in prior tensor models, including infinite families of dominant graphs, and set the stage for deeper renormalization and Schwinger-Dyson analyses in this broader invariant class.

Abstract

We study a sextic tensor model where the interaction terms are given by all -invariant bubbles. The class of invariants studied here is thus a larger one that the class of the -invariant sextic tensor model. We implement the large limit mechanism for this general model and we explicitly identify the dominant graphs in the expansion. This class of dominant graphs contains tadpole graphs, melonic graphs but also new types of tensor graphs. Our analysis adapts the tensorial intermediate field method, previously applied only to the prismatic interaction, to all connected sextic interactions except the wheel interaction, which we treat separately using a cycle analysis.
Paper Structure (21 sections, 35 equations, 39 figures)

This paper contains 21 sections, 35 equations, 39 figures.

Table of Contents

  1. Introduction
  2. The general sextic model
  3. The action of the model
  4. Inequivalent cycles
  5. Intermediate field method for sextic interactions
  6. Real intermediate field
  7. Complex intermediate field
  8. No mixing of the wheel interaction
  9. The WT cycle.
  10. The WTT cycle.
  11. The WWT cycle.
  12. Identification of the dominant graphs of the general model
  13. The prismatic interaction
  14. The wheel interaction
  15. The I3 and I4 interaction
  16. ...and 6 more sections

Figures (39)

  • Figure 1: The $O(N)^3$-invariant sextic interactions. Color permutations are implicit.
  • Figure 2: Example of a 2-cycle visiting a wheel and a prism in the Feynman (left) and bubble (right) representation, $\mathcal{C}_2 = \langle (w_2, p_1), (p_4, w_4)\rangle$.
  • Figure 3: Tetrahedric term $\hat{I}_T(T,\chi)$ with an intermediate field.
  • Figure 4: Decomposition of the prismatic interaction using a real intermediate field $\chi^{(1)}_{abc}$.
  • Figure 5: Pillow term $\hat{I}_P^{(a)}(T,\chi)$ with an intermediate field.
  • ...and 34 more figures