Related papers: Noncommutative Field Theory: Numerical Analysis wi…
We study a fourth-order derivative scalar field configuration in a fixed Lifshitz background. Using an auxiliary field we rewrite the equations of motion as two coupled second order equations. We specialize to the limit that the mass of the…
Quantum Space-Time and Phase Space with fuzzy geometric structure are studied as possible formalism for quantization of massive particles and fields. In this approach the state of nonrelativistic particle m described by the fuzzy point of…
We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which -- in contrast to the well known Moyal-Weyl deformation -- lead to a theory with modified…
We study renormalization in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model, where the matrix size plays the role of a UV cutoff. We define correlation functions by using the Berezin symbol identified…
Diffeomorphisms can be seen as automorphisms of the algebra of functions. In the matrix regularization, functions on a smooth compact manifold are mapped to finite size matrices. We consider how diffeomorphisms act on the configuration…
We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.
The 2d gauge theory on the lattice is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point…
The fuzzy-sphere regularization is an emerging numerical and theoretical technique for studying conformal field theories (CFTs). In this paper, we apply it to the $O(N)$ vector model, one of the most prominent theories for critical behavior…
We study relations between different kinds of non-commutative spheres which have appeared in the context of ADS/CFT correspondences recently, emphasizing the connections between spaces that have manifest quantum group symmetry and spaces…
Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with…
We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in two-dimensional noncommutative scalar field…
We study thermal effects for a noncommutative real scalar field in 2+1 dimensions including a Grosse-Wulkenhaar term. Using a perturbative expansion for the free energy, we deduce some general properties of the corresponding contributions,…
We use Monte Carlo simulations to study a dynamically triangulated disk with Ising spins on the vertices and a boundary magnetic field. For the case of zero magnetic field we show that the model possesses three phases. For one of these the…
We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…
Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study,…
We study the fate of the fuzzy sphere vacuum solutions in the SU(N)xSU(N+M) Klebanov-Strassler theory at finite temperature and at weak coupling. We find that thermal effects push the S^2 radius --a modulus at T=0-- towards vanishing size.…
We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In…
We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally…
We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms.…
We study solitons in scalar theories with polynomial interactions on the fuzzy sphere. Such solitons are described by projection operators of rank k, and hence the moduli space for the solitons is the Grassmannian Gr(k,2j+1). The gradient…