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Noncommutative BTZ black hole and discrete time
Get PDFWe search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to R × S^1 symplectic leaves, where R is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator
General computations without fixing the gauge
Get PDFWithin the framework of a manifestly gauge invariant exact renormalization group for SU(N) Yang-Mills, we derive a simple expression for the expectation value of an arbitrary gauge invariant operator. We illustrate the use of this formula by computing the O(g^2) correction to the rectangular, Euclidean Wilson loop with sides T >> L. The standard result is trivially obtained, directly in the continuum, for the first time without fixing the gauge. We comment on possible future applications of the formalism
Monte Carlo Simulation of a NC Gauge Theory on the Fuzzy Sphere
Get PDFWe find using Monte Carlo simulation the phase structure of noncommutative U(1) gauge theory in two dimensions with the fuzzy sphere S^2_N as a non-perturbative regulator. There are three phases of the model. i) A matrix phase where the theory is essentially SU(N) Yang-Mills reduced to zero dimension. ii) A weak coupling fuzzy sphere phase with constant specific heat and iii) A strong coupling fuzzy sphere phase with non-constant specific heat. The order parameter distinguishing the matrix phase from the sphere phase is the radius of the fuzzy sphere. The three phases meet at a triple point. We also give the theoretical one-loop and 1/N expansion predictions for the transition lines which are in good agreement with the numerical data. A Monte Carlo measurement of the triple point is also given
Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
Get PDFAfter reviewing the construction of the fuzzy sphere and the formulation of the scalar theory in this non-commutative setting, we address a detailed non-perturbative study by means of a novel algorithm, which strongly reduces the correlation problems in the matrix update process, and which allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the rôle they play in the case when the potential admits classically degenerate minima, pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. We also investigate the effects of the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere
Self-dual instanton and nonself-dual instanton-antiinstanton solutions in d=4 Yang-Mills theory
Get PDFSubjecting the SU(2) Yang–Mills system to azimuthal symmetries in both the x − y and the z − t planes results in a residual subsystem described by a U(1) Higgs like model with two complex scalar fields on the quarter plane. The resulting instantons are labeled by integers (m,n_1,n_2) with topological charges q = (1/2)[1 − (−1)^m](n_1)(n_2). Solutions are constructed numerically for m = 1, 2, 3 and a range of n 1 = n 2 = n. It is found that only the m = 1 instantons are self-dual, the m > 1 configurations describing composite instanton-antiinstanton lumps
An analytic equation of state for Ising-like models
Get PDFUsing an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, y = f(x), that exhibits all desired asymptotic and analyticity properties in the three limits x → 0, x → ∞ and x → −1. The only necessary inputs are the Wilson functions γ_λ , γ_φ and γ_(φ^2) , associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N = 1, we derive a one-loop equation of state for 2 < d < 4 naturally parameterized by a ratio of non-linear scaling fields. For d = 3 we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes
Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model
Get PDFWe study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping Bose-Hubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case [BD], we observe here new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at some fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the BEC suppression at integer densities may disappear, if disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases
Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
Get PDFWe review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution
Spinning U(1) gauged Skyrmions
Get PDFWe construct axially symmetric solutions of U(1) gauged Skyrme model. Possessing a nonvanishing magnetic moment, these solitons have also a nonzero angular momentum proportional to the electric charge
Noncommutative Two Dimensional Gravities
Get PDFWe give formulations of noncommutative two dimensional gravities in terms of noncommutative gauge theories. We survey their classical solutions and show that solutions of the corresponding commutative theories continue to be solutions in the noncommutative theories as well. We argue that the existence of “twisted” diffeomorphisms, recently introduced in [1], is crucial for this conclusion