Related papers: Bosonic Tensor Models at Large $N$ and Small $\eps…
We perform a non-perturbative study of the scale-dependent renormalisation factors of a complete set of dimension-six four-fermion operators. The renormalisation-group (RG) running is determined in the continuum limit for a specific…
The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) expanded in large spin S have the asymptotics \gamma= f ln S + f_c + 1/S (f_11 ln S + f_10) + ..., where f (the universal scaling function or cusp anomaly),…
The disorder operator, as an easily measured non-local observable, displays great potential in detecting intrinsic information of field theories. It has been systematically studied in 1d and 2d quantum systems, while the knowledge of 3d is…
We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism…
Critical behaviour of the O(n)-symmetric $\phi^{4}$-model with an antisymmetric tensor order parameter is studied by means of the field-theoretic renormalization group (RG) in the leading order of the $\varepsilon=4-d$-expansion (one-loop…
We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $\phi_i$ transforming as an $O(N)$ vector. The crossing symmetry of the…
In this paper, we continue the study of large $N$ problems for the Wick renormalized linear sigma model, i.e. $N$-component $\Phi^4$ model, in two spatial dimensions, using stochastic quantization methods and Dyson--Schwinger equations. We…
We demonstrate the renormalisability of quantum field theories in four dimensions with elementary self-interacting Dirac fermions and to leading order in the limit of many fermion flavours $N_{\rm f}$. Starting from the underlying…
Type 0A string theory in the (2,4k) superconformal minimal model backgrounds and the bosonic string in the (2,2k-1) conformal minimal models, while perturbatively identical in some regimes, may be distinguished non-perturbatively using…
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…
We consider certain orbifoldization of the ${\cal N}=4$ field theories that leads to ${\cal N}=2,1,0$ field theories in 4 dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in…
We advance the multipoint lightcone bootstrap and compute anomalous dimensions of triple-twist operators at large spin. In contrast to the well-studied double-twist operators, triple-twist primaries are highly degenerate so that their…
In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge $n$ operator in the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$ can be computed semiclassically for arbitrary values of $\lambda n$,…
Large-$S$ and large-$N$ theories (spin value $S$ and spinor component number $N$) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-$S$ spin-wave theory captures the correct semiclassical behavior,…
A cutoff version of the $\lambda \phi^4$ O(N) model is considered to leading order in 1/N with particular attention to the effective potential, which is surprisingly rich in structure. With suitable restriction on a background classical…
We analyze the constraints on the general form and the singularity structure of the correlation functions of the symmetric, traceless and conserved stress-energy tensor implied by conformal invariance and higher spin symmetry in four…
We demonstrate that random tensors transforming under rank-$5$ irreducible representations of $\mathrm{O}(N)$ can support melonic large $N$ expansions. Our construction is based on models with sextic ($5$-simplex) interaction, which…
The density of states for the Schroedinger equation with a Gaussian random potential is determined by the functional integral corresponding to the phi^4 theory with a `wrong' sign of the interaction constant. The special role of the…
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (QED$_3$) coupled to $N_f=4$ two-component Dirac fermions. Specifically, we study the four-point…