1,721,006 research outputs found
One loop beta functions and fixed points in higher derivative sigma models
Full text linkWe calculate the one loop beta functions for nonlinear sigma models in four dimensions containing general two and four derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N geq 4. In the chiral SU(N) models there are in general six couplings, but only five for N=3 and four for N=2; we find fixed points only for N=2,3. In the approximation considered, the four derivative couplings are asymptotically free but the coupling in the two derivative term has a nonzero limit. These results support the hypothesis that certain sigma models may be asymptotically safe
Consequences of gauging the Weyl symmetry and the two-dimensional conformal anomaly
No full textWe discuss the generalization of the local renormalization group approach to theories in which Weyl symmetry is gauged. These theories naturally correspond to scale-invariant - rather than conformal-invariant - models in the flat-space limit. We argue that this generalization can be of use when discussing the issue of scale vs conformal invariance in quantum and statistical field theories. The application of Wess-Zumino consistency conditions constrains the form of the Weyl anomaly and the beta functions in a nonperturbative way. In this work, we concentrate on two-dimensional models including also the contributions of the boundary. Our findings suggest that the renormalization group flow between scale-invariant theories differs from the one between conformal theories because of the presence of a new charge that appears in the anomaly. It does not seem to be possible to find a general scheme for which the new charge is zero, unless the theory is conformal in flat space. Two illustrative examples involving flat space's conformal- and scale-invariant models that do not allow for a naive application of the standard local treatment are given
Renormalization group flow of hexatic membranes
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121474.pdf (Author’s version preprint ) (Open Access
On the non-local heat kernel expansion
Full text linkWe propose a novel derivation of the non-local heat kernel expansion, first studied by Barvinsky, Vilkovisky, and Avramidi, based on simple diagrammatic equations satisfied by the heat kernel. For Laplace-type differential operators, we obtain the explicit form of the non-local heat kernel form factors to second order in the curvatures. Our method can be generalized easily to the derivation of the non-local heat kernel expansion of a wide class of differential operators. © 2013 American Institute of Physics
Fluid Membranes and 2d Quantum Gravity
Full text linkWe study the RG flow of two dimensional (fluid) membranes embedded in Euclidean D-dimensional space using functional RG methods based on the effective average action. By considering a truncation ansatz for the effective average action with both extrinsic and intrinsic curvature terms, we derive a system of beta functions for the running surface tension µk, bending rigidity κk, and Gaussian rigidity κ̄k. We look for non-trivial fixed points but we find no evidence for a crumpling transition at T 6 = 0. Finally, we propose to identify the D → 0 limit of the theory with two dimensional quantum gravity. In this limit, we derive new beta functions for both cosmological and Newton’s constants
Erratum: The renormalization of fluctuating branes, the Galileon and asymptotic safety (Journal of High Energy Physics (2013) 04, (036))
No full textScheme dependence and universality in the functional renormalization group
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130228.pdf (Publisher’s version ) (Open Access
Spectral dimensions from the spectral action
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139590pub.pdf (Publisher’s version ) (Open Access)
Contains fulltext :
139590.pdf (Author’s version preprint ) (Open Access
Projective transformations in metric-Affine and Weylian geometries
No full textWe discuss generalizations of the notions of projective transformations acting on affine model of Riemann-Cartan and Riemann-Cartan-Weyl gravity which preserve the projective structure of the light-cones. We show how the invariance under some projective transformations can be used to recast a Riemann-Cartan-Weyl geometry either as a model in which the role of the Weyl gauge potential is played by the torsion vector, which we call torsion-gauging, or as a model with traditional Weyl (conformal) invariance
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