Giorgini, L.T. Jentschura, U.D. Malatesta, E.M. Parisi, G. Rizzo, T. Zinn-Justin, J.

For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory is increased. This problem is exacerbated by the fact that perturbation series derived from loop diagram (Feynm...

Córdova, Lucía He, Yifei Kruczenski, Martin Vieira, Pedro
Published in
Journal of High Energy Physics

We consider the scattering matrices of massive quantum field theories with no bound states and a global O(N) symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass m transforming in the vector representation as restricted by the general conditions of unitarity, crossing, analyticity an...

Binder, Damon J. Rychkov, Slava
Published in
Journal of High Energy Physics

When studying quantum field theories and lattice models, it is often useful to analytically continue the number of field or spin components from an integer to a real number. In spite of this, the precise meaning of such analytic continuations has never been fully clarified, and in particular the symmetry of these theories is obscure. We clarify the...

Benedetti, Dario Costa, Ilaria

We study classical and quantum (at large-$N$) field equations of bosonic tensor models with quartic interactions and $O(N)^3$ symmetry. Among various possible patterns of spontaneous symmetry breaking we highlight an $SO(3)$ invariant solution, with the tensor field expressed in terms of the Wigner $3jm$ symbol. We argue that such solution has a sp...

Benedetti, Dario Gurau, Razvan Suzuki, Kenta

We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $\phi^4$ composite operators, known as tetrahedron, pillow and double-trace. As shown in arXiv:1903.03578 and arXiv:1909.07767, the tetrahedron operator is exactly marginal in the large-$N$ ...

Fleming, C. Delamotte, B. Yabunaka, S.

We study the $O(N)$ model in dimension three (3$d$) at large and infinite $N$ and show that the line of fixed points found at $N=\infty$ --the Bardeen-Moshe-Bander (BMB) line-- has an intriguing origin at finite $N$. The large $N$ limit that allows us to find the BMB line must be taken on particular trajectories in the $(d,N)$-plane: $d=3-\alpha/N$...

De Polsi, Gonzalo Balog, Ivan Tissier, Matthieu Wschebor, Nicolás

We compute the critical exponents $\nu$, $\eta$ and $\omega$ of $O(N)$ models for various values of $N$ by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted $\mathcal{O}(\partial^4)$]. We analyze the behavior of this approximation scheme at successive orders and o...

Benedetti, Dario Delporte, Nicolas Harribey, Sabine Sinha, Ritam

We study bosonic tensor field theories with sextic interactions in $d

De Polsi, Gonzalo Tissier, Matthieu Wschebor, Nicolás

It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated vector operator, invariant under all internal symmetries of the model, with scaling dimension $-1$. In this article, we compute the scaling dimensions of vector operator...

Ben Geloun, Joseph

Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle to study their combinatorial, topological and algebraic properties. We give here an overview of the symmetric ...