1207 research outputs found
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Point Interactions in One Dimension and Holonomic Quantum Fields
Get PDFWe introduce and study a family of quantum fields, associated to δ-interactions in one dimension. These fields are analogous to holonomic quantum fields of M. Sato, T. Miwa and M. Jimbo. Corresponding field operators belong to an infinite-dimensional representation of the group SL(2,R) in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the det*-bundle over a Grassmannian associated to a family of Schroedinger operators
Fuzzy toric geometries
Get PDFWe describe a construction of fuzzy spaces which approximate projective toric varieties. The construction uses the canonical embedding of such varieties into a complex projective space: The algebra of fuzzy functions on a toric variety is obtained by a restriction of the fuzzy algebra of functions on the complex projective space appearing in the embedding. We give several explicit examples for this construction; in particular, we present fuzzy weighted projective spaces as well as fuzzy Hirzebruch and del Pezzo surfaces. As our construction is actually suited for arbitrary subvarieties of complex projective spaces, one can easily obtain large classes of fuzzy Calabi-Yau manifolds and we comment on fuzzy K3 surfaces and fuzzy quintic three-folds. Besides enlarging the number of available fuzzy spaces significantly, we find evidence for the conjecture that the fuzzification of a projective toric variety amounts to a quantization of its toric base
High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model
Get PDFMotivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study inter-faces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation
Non-Abelian Solutions in AdS4 and d=11 Supergravity
Get PDFWe consider solutions of the four dimensional Einstein-Yang-Mills system with a negative cosmological constant Λ = −3g^2 , where g is the nonabelian gauge coupling constant. This theory corresponds to a consistent truncation of N = 4 gauged supergravity and may be uplifted to d = 11 supergravity. A systematic study of all known solutions is presented as well as new configurations corresponding to rotating regular dyons and rotating nonabelian black holes. The thermodynamics of the static black hole solutions is also discussed. The generic EYM solutions present a nonvanishing magnetic flux at infinity and should give us information about the structure of a CFT in a background SU(2) field. We argue that the existence of these configurations violating the no hair conjecture is puzzling from the AdS/CFT point of view
Lowest Lyapunov Exponents for the Armchair Nanotube
Get PDFWe compute sum of the two the lowest Lyapunov exponents γ_(2N−1) + γ_2N of a tight-binding model for an single-wall armchair carbon nanotube with point impurities to lowest (second) order in the disorder parameter λ. The result is that γ_(2N−1) + γ_2N ∼ (λ^2)(N^−1) , where N is the number of hexagons around the perimeter. This is similar to the result of Schulz-Baldes [20] for the standard Anderson model on a strip, but because there are only two conducting channels near the Fermi level (centre of the spectral band), this implies that the scattering length is proportional to the diameter of the tube as predicted by Todorov and White [10]
Asymptotic Feynman-Kac Formulae for large Symmetrised systems of Random Walks
Get PDFWe study large deviations principles for N random processes on the lattice Z_d with finite time horizon [0, β] under a symmetrised measure where all initial and terminal points are uniformly given by a random permutation. That is, given a permutation σ of N elements and a vector (x_1 , . . . , x_N) of N initial points we let the random processes terminate in the points (x_σ(1) , . . . , x_σ(N)) and then sum over all possible permutations and initial points, weighted with an initial distribution. There is a two-level random mechanism and we prove two-level large deviations principles for the mean of empirical path measures, for the mean of paths and for the mean of occupation local times under this symmetrised measure. The symmetrised measure cannot be written as any product of single random process distributions. We show a couple of important applications of these results in quantum statistical mechanics using the Feynman-Kac formulae representing traces of certain trace class operators. In particular we prove a non-commutative Varadhan Lemma for quantum spin systems with Bose-Einstein statistics and mean field interactions. A special case of our large deviations principle for the mean of occupation local times of N simple random walks has the Donsker-Varadhan rate function as the rate function for the limit N → ∞ but for finite time β. We give an interpretation in quantum statistical mechanics for this surprising result
Quantization of Flag Manifolds and their Supersymmetric Extensions
Get PDFWe first review the description of flag manifolds in terms of Plücker coordinates and coherent states. Using this description, we construct fuzzy versions of the algebra of functions on these spaces in both operatorial and star product language. Our main focus is here on flag manifolds appearing in the double fibrations underlying the most common twistor correspondences. After extending the Plücker description to certain supersymmetric cases, we also obtain the appropriate deformed algebra of functions on a number of fuzzy flag supermanifolds. In particular, fuzzy versions of Calabi-Yau supermanifolds are found
Nonlocal regularisation of noncommutative field theories
Get PDFWe study noncommutative field theories, which are inherently nonlocal, using a Poincaré-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cut-off scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention onto the particular case when the noncommutativity parameter is inversely proportional to the square of the cut-off, via a dimensionless parameter η. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in η-dependent terms. The implications of this approach, which avoids the problems related to UV-IR mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories
Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
Get PDFWe generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space