Related papers: $SO(3)$-invariant phase of the $O(N)^3$ tensor mod…

We study the $O(N)^3$ supersymmetric quantum field theory of a scalar superfield $\Phi_{abc}$ with a tetrahedral interaction. In the large $N$ limit the theory is dominated by the melonic diagrams. We solve the corresponding Dyson-Schwinger…

Recent numerical and theoretical studies on the two-dimensional $J$-$Q_3$ model suggests that the deconfined quantum critical point is actually a $SO(5)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $O(4)$.…

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's…

We study the $O(N)^3$ symmetric quantum field theory of a bosonic tensor $\phi^{abc}$ 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…

This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…

It has recently been proven that in rank three tensor models, the anti-symmetric and symmetric traceless sectors both support a large $N$ expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how to extend these results…

In this paper we study the large N limit of the $O(N)$-invariant linear sigma model, which is a vector-valued generalization of the $\Phi^4$ quantum field theory, on the three dimensional torus. We study the problem via its stochastic…

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…

We study the $O(N_1)\times O(N_2)\times O(N_3)$ symmetric quantum mechanics of 3-index Majorana fermions. When the ranks $N_i$ are all equal, this model has a large $N$ limit which is dominated by the melonic Feynman diagrams. We derive an…

We study spontaneous breaking of scale invariance in the large N limit of three dimensional $U(N)_\kappa$ Chern-Simons theories coupled to a scalar field in the fundamental representation. When a $\lambda_6(\phi^\dagger\cdot\phi)^3$ self…

For some theories where the degrees of freedom are tensors of rank $3$ or higher, there exist solvable large $N$ limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank-$3$ tensor in the…

We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to…

We construct an off-shell N=3 supersymmetric extension of the abelian D=4 Born-Infeld action starting from the action of supersymmetric Maxwell theory in N=3 harmonic superspace. A crucial new feature of the N=3 super BI action is that its…

We study the double scaling limit of the $O(N)^3$-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types of quartic invariants, the tetrahedric…

We include a new 7-form ansatz in 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is considered as a U(1) bundle on CP^3. After a general analysis of the ansatz, we take a special form of it and obtain a scalar…

Perturbing the standard Gross-Neveu model for $N^3$ fermions by quartic interactions with the appropriate tensorial contraction patterns, we reduce the original $U(N^3)$ symmetry to either $U(N)\times U(N^2)$ or $U(N)\times U(N)\times…

The search for classical or quantum combinatorial invariants of compact n-dimensional manifolds (n=3,4) plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition…

We study the three dimensional O(N) invariant bosonic vector model with a $\frac{\lambda}{N}(\phi^{a}\phi^{a})^{2}$ interaction at its infrared fixed point, using a bilocal field approach and in an $1/N$ expansion. We identify a (negative…

We study regular self-gravitating non-topological soliton solutions of the $U(1)$ gauged non-linear $O(3)$ sigma model with the usual kinetic term and a simple symmetry breaking potential in 3+1 dimensional asymptotically flat spacetime.…

We construct a new SO(3)$\times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear…