170 research outputs found
Fixed-point structure and effective fractional dimensionality for O(N) models with long-range interactions
No full textWe study, by renormalization group methods, O(N) models with interactions decaying as power law with exponent d + sigma. When only the long-range momentum term p(sigma) is considered in the propagator, the critical exponents can be computed from those of the corresponding short-range O(N) models at an effective fractional dimension D-eff. Neglecting wave function renormalization effects the result for the effective dimension is D-eff = 2d/sigma, which turns to be exact in the spherical model limit (N -> 8). Introducing a running wave function renormalization term the effective dimension becomes instead D-eff = (2-eta SR)d/sigma . The latter result coincides with the one found using standard scaling arguments. Explicit results in two and three dimensions are given for the exponent nu. We propose an improved method to describe the full theory space of the models where both short-and long-range propagator terms are present and no a priori choice among the two in the renormalization group flow is done. The eigenvalue spectrum of the full theory for all possible fixed points is drawn and a full description of the fixed-point structure is given, including multicritical long-range universality classes. The effective dimension is shown to be only approximate, and the resulting error is estimated
Fixed points of nonlinear sigma models in d>2
No full textAbstractUsing Wilsonian methods, we study the renormalization group flow of the nonlinear sigma model in any dimension d, restricting our attention to terms with two derivatives. At one loop we always find a Ricci-type flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For d>2 and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned
Renormalization group flow equations for the proper vertices of the background effective average action
No full textWe derive a system of coupled flow equations for the proper vertices of the background effective average action and we give an explicit representation of these by means of diagrammatic and momentum space techniques. This explicit representation can be used as a new computational technique that enables the projection of the flow of a large new class of truncations of the background effective average action. In particular, these can be single- or bifield truncations of local or nonlocal character. As an application we study non-Abelian gauge theories. We show how to use this new technique to calculate the beta function of the gauge coupling ( without employing the heat kernel expansion) under various approximations. In particular, one of these approximations leads to a derivation of beta functions similar to those proposed as candidates for an "all- orders" beta function. Finally, we discuss some possible phenomenology related to these flows
Leading gravitational corrections and a unified universe
No full textLeading order gravitational corrections to the Einstein-Hilbert action can lead to a consistent picture of the universe by unifying the epochs of inflation and dark energy in a single framework. While the leading local correction induces an inflationary phase in the early universe, the leading nonlocal term leads to an accelerated expansion of the universe at the present epoch. We argue that both the leading UV and IR terms can be obtained within the framework of a covariant effective field theory of gravity. The perturbative gravitational corrections therefore provide a fundamental basis for understanding a possible connection between the two epochs.</p
On the non-local heat kernel expansion
No full textWe 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
Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram
No full textWe present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z(2)-scalar theories. The idea is to perform the path integral by weighting the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we are integrating. We show that depending on the initial condition, or initial point in the phase diagram, we obtain different behaviors of the four-point function at the endpoint of the flow
A unified universe
No full textAbstract We present a unified evolution of the universe from very early times until the present epoch by including both the leading local correction R2 and the leading non-local term R1□2R to the classical gravitational action. We find that the inflationary phase driven by R2 term gracefully exits in a transitory regime characterized by coherent oscillations of the Hubble parameter. The universe then naturally enters into a radiation dominated epoch followed by a matter dominated era. At sufficiently late times after radiation–matter equality, the non-local term starts to dominate inducing an accelerated expansion of the universe at the present epoch. We further exhibit the fact that both the leading local and non-local terms can be obtained within the covariant effective field theory of gravity. This scenario thus provides a unified picture of inflation and dark energy in a single framework by means of a purely gravitational action without the usual need of a scalar field
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