Related papers: Bosonic Tensor Models at Large $N$ and Small $\eps…
We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials…
The magnetic line defect in the $O(N)$ model gives rise to a non-trivial one-dimensional defect conformal field theory of theoretical and experimental value. This model is considered here in $d=4-\varepsilon$ and the full spectrum of defect…
In an arbitrary unitary 4D CFT we consider a scalar operator \phi, and the operator \phi^2 defined as the lowest dimension scalar which appears in the OPE \phi\times\phi with a nonzero coefficient. Using general considerations of OPE,…
We consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of…
We study fixed-points of scalar fields that transform in the bifundamental representation of $O(N)\times O(M)$ in $3-\epsilon$ dimensions, generalizing the classic tricritical sextic vector model. In the limit where $N$ is large but $M$ is…
We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the…
The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-component fields and corresponding multi-index…
Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. Some models allowing a $1/N$ expansion have been explored, most of them generating branched-polymer geometries. Recently, enhancements…
The theory of quaternionic operators has applications in several different fields such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and…
We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed $\mathcal{N}=4$ SYM theory. We show…
The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO)…
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative…
Free tensors are tensors which, after a change of bases, have free support: any two distinct elements of its support differ in at least two coordinates. They play a distinguished role in the theory of bilinear complexity, in particular in…
We study a large $N$ tensor model with $O(N)^3$ symmetry containing two flavors of Majorana fermions, $\psi_1^{abc}$ and $\psi_2^{abc}$. We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev models, each one…
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new…
Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes…
Large $N$ quasifermionic ($QF$) Chern-Simons-matter theories exhibit weakly-broken higher-spin symmetry and contain an infinite-dimensional algebra of almost-conserved higher-spin currents. By analyzing local higher-spin Ward identities, we…
Tensor models generalize matrix models and generate colored triangulations of pseudo-manifolds in dimensions $D\geq 3$. The free energies of some models have been recently shown to admit a double scaling limit, i.e. large tensor size $N$…
We study the cubic fixed point for $N=3$ and $4$ by using finite size scaling applied to data obtained from Monte Carlo simulations of the $N$-component $\phi^4$ model on the simple cubic lattice. We generalize the idea of improved models…
We consider the conformal dimension of an operator with large spin, using a spinning D3-brane with electric flux in AdS_5 x S^5 instead of spinning fundamental string. This spinning D3-brane solution seems to correspond to an operator made…