Related papers: $O(N)$ Models with Boundary Interactions and their…
We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a…
For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-invariant quadratic term contains small non-nearest-neighbour…
We develop a framework to simulate quantum field theories (QFTs) with boundaries in $(1+1)$-dimenmsional curved spacetimes by employing open spin systems. Building upon our previous work that established a mapping from spin systems to QFTs…
We consider replicated $O(N)$ symmetry in two dimensions within the exact framework of scale invariant scattering theory and determine the lines of renormalization group fixed points in the limit of zero replicas corresponding to quenched…
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…
We study the $O(N)$ non-linear $\sigma$ model on three-dimensional manifolds of constant curvature by means of the large $N$ expansion at the critical point. We examine saddle point equations imposing anti-periodic boundary condition in…
We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and…
We review some recent work on AdS/CFT duality involving the 3d O(N) Vector Model and AdS4 Higher Spin Gravity. Our construction is based on bi-local collective field theory which provides an off-shell formulation of Higher Spin Gravity with…
The extraordinary transition which occurs in the two-dimensional O(n) model for $n<1$ at sufficiently enhanced surface couplings is studied by conformal perturbation theory about infinite coupling and by finite-size scaling of the spectrum…
The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed…
This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2…
We study the critical behavior at the ordinary surface universality class of the three-dimensional O($N$) model, bounded by a two-dimensional surface. Using high-precision Monte Carlo simulations of an improved lattice model, where the…
We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for D->1, while N->0 leads to self-avoiding tethered membranes (as the O(N) model reduces to…
We show that the large $n$ limit of the $O(n)$ quantum rotor model defined on a general graph has the same critical behavior as the corresponding quantum spherical model and that the critical exponents depend solely on the spectral…
We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete…
We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for…
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 investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases…
We explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface transitions of the 3d Ising and other O(N) models through…
Field theory at nonvanishing temperature beyond perturbation theory is discussed for the $N$-component $O(N)$-symmetric scalar theory. We compute the effective potential directly in three dimensions using an exact evolution equation for an…