Bootstrapping Tensor Integrals
Nathan Pagliaroli, Carlos I. Pérez-Sánchez, Brayden Smith
TLDR
This paper introduces a bootstrapping with positivity method to approximate moments of random U(N)^D invariant tensors in the large N limit.
Key contributions
- Proposes a "bootstrapping with positivity" method for U(N)^D invariant tensors.
- Combines Dyson-Schwinger equations and positivity constraints to approximate tensor moments.
- Successfully bootstraps quartic and hexic rank three tensor models, demonstrating quick convergence.
- Conjectures new explicit formulae for rank three quartic model moments, supported by bootstrapped results.
Why it matters
This work extends the successful bootstrapping approach from random matrices to random tensors, a crucial step for understanding quantum gravity and holographic dualities. The proposed method provides a powerful tool for calculating moments and offers new explicit formulae, advancing theoretical physics.
Original Abstract
This work proposes a bootstrapping with positivity methodology to study random $U(N)^{D}$ invariant tensors in the large $N$ limit. As has been done for $U(N)$ invariant random matrices, we combine the Dyson-Schwinger equations and positivity constraints of moments to approximate the moments of such tensor models. As examples, we bootstrap the quartic and two hexic rank three tensor models. All models studied converge quickly, and for those which have known analytic formulae, they converge to such solutions. We conjecture new explicit formulae for all moments of the rank three quartic model and support this conjecture using bootstrapped results and explicit double-series computations with 'feyntensor'.
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