Related papers: Exact Operator Map from Strong Coupling to Free Fi…
Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal…
We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction. A bare mass is required for the theory to…
We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a "foliation" of $\mathbb{R}^3$ into fuzzy spheres. We first construct a natural matrix base adapted to…
We develop a systematic renormalization procedure for QFT in anti-de Sitter spacetime. UV infinities are regulated using a geodesic point-splitting method, which respects AdS isometries, while IR infinities are regulated by cutting off the…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
We demonstrate that, by utilizing the boundary conformal field theory (BCFT) operator algebra of the Liouville CFT, one can express its path-integral on any Riemann surface as a three dimensional path-integral with appropriate boundary…
We present and discuss a conjectured criterion for determining whether a 4d quantum field theory is IR free, or flows to an interacting conformal field theory in the infrared: ``the correct infrared phase is that with the larger conformal…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
We explore the space of non-gravitational, maximally supersymmetric, planar 4d effective field theories (EFTs) that have $\mathcal{N}=4$ super Yang-Mills (SYM) at leading order. We show that in the weakly-coupled regime, highly non-trivial…
We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the Truncated Conformal Space Approach (TCSA), a Hamiltonian method which exploits the conformal structure of the…
We consider a scalar quantum field theory with global $O(N)^3$ symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-N limit. For imaginary tetrahedral coupling the theory is asymptotically free, with…
We provide a concise description of our recent work on the exact conformal field theory (CFT) formulation of the superstring in the pp-wave background with Ramond-Ramond (RR) flux, using the Green-Schwarz formalism in the semi-light-cone…
This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
In this paper we construct Seiberg-Witten maps for superfields on canonically deformed N=1, d=4 Minkowski and Euclidean superspace. On Minkowski superspace we show that the Seiberg-Witten map is not compatible with locality, (anti)chirality…
A vector subspace $\cls$ of $\IM_n(\IC)$ is called unital operator system if $x \in \cls$ if and only if $x^* \in \cls$ and the identity operator $I_n \in \cls$, where $n$ is any fixed positive integer. Let $C^*(\cls)$ be the $C^*$…
We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of a no-pair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential.…
We work out the interplay between lowest-order perturbative computations in the 't Hooft coupling, $g^2=g^2_{YM} N$, operator mixing, renormalization-group (RG) improved ultraviolet (UV) asymptotics of leading-order (LO) nonplanar/planar…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
Starting from a local quantum field theory with an unbroken compact symmetry group $G$ in 1+1-dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region.…