1,720,998 research outputs found
Selected applications of functional RG
Full text linkIn this thesis we will address the study of quantum field theories using the exact renormalization group technique. In particular, we will calculate the flow of a Yukawa system coupled to gravity and that of a higher derivative nonlinear sigma model. The study of the Yukawa system in presence of gravity, as well as the study of any matter theory coupled to gravity, is important for two reason. First, it is interesting to see what gravitational dressing one should expect to the beta functions of any matter theory. Second, it is important to test the possibility that gravity is an asymptotically safe theory [1, 2] against the addition of matter degrees of freedom. We also calculate the 1-loop flow of a general higher derivative nonlinear sigma model, using exact renormalization group techniques. We think that the nonlinear sigma model is an important arena to test the exact renormalization. The reason is that the nonlinear sigma model shares many of the features of gravity, like perturbative nonrenormalizability, but does not have the additional complication of a local gauge invariance. Furthermore, it is an interesting question whether a nonlinear sigma model admits a ultraviolet limit or it has to be regarded as an effective field theory only.
The plan of the work is as follows. In Chapter 1 we give a very brief introduction to the technique of functional exact renormalization group. In Chapter 2 we introduce the notion of “Asymptotic Safety” [1] and discuss some of the approximation schemes generally involved in calculations. In Chapter 3 we use a simple Yukawa model as a toy model for many of the techniques we will need later. We also discuss the background field method in the context of a theory with local gauge invariance, which will turn out to be useful in Chapter 4. In Chapter 4 we couple the simple Yukawa model with gravity and calculate its renormalization group flow. In Chapter 5 we study numerically the flow calculated in Chapter 4 and point out the possibility that the model admits a nontrivial ultraviolet limit. Chapter 6 is the final chapter and contains the study of the flow of the higher derivative nonlinear sigma model; it is a self contained chapter. In fact, Chapter 5 and 6 contain separate discussions for the results of the Yukawa and sigma model, respectively. We dedicate the appendices to arguments that would have implied very long digressions in the main text
Asymptotic safety in einstein gravity and scalar-fermion matter
Full text linkWithin the functional renormalization group approach we study the effective quantum field theory of Einstein gravity and one self-interacting scalar coupled to Nf Dirac fermions. We include in our analysis the matter anomalous dimensions induced by all the interactions and analyze the highly nonlinear beta functions determining the renormalization flow. We find the existence of a nontrivial fixed point structure both for the gravity and the matter sector, besides the usual Gaussian matter one. This suggests that asymptotic safety could be realized in the gravitational sector and in the standard model. Nontriviality in the Higgs sector might involve gravitational interactions. © 2010 The American Physical Society
Effective models of membranes from symmetry breaking
Full text linkWe show how to obtain all the models of the continuous description of membranes by constructing the appropriate nonlinear realizations of the Euclidean symmetries of the embedding. The procedure has the advantage of giving a unified formalism with which the models are generated and highlights the relevant order parameters in each phase. We use our findings to investigate a fluid description of both tethered and hexatic membranes, showing that both the melting and the loss of local order induce long-range interactions in the high-temperature fluid phase. The results can be used to understand the appearance of intrinsic ripples in crystalline membranes in a thermal bath
Composite higher derivative operators in d=2+epsilon dimensions and the spectrum of asymptotically safe gravity
No full textWe discuss the renormalization of Einstein -Hilbert gravity in d = 2 + e dimensions. We show that the application of the path -integral approach leads naturally to scheme- and gauge -independent results on shell, but also gives a natural notion of quantum metric off shell, which is the natural argument of the effective action, even at the leading order in perturbation theory. The renormalization group of Newton's constant is consistent with the asymptotic safety scenario for quantum gravity in that it has a UV -relevant fixed point. We extend the approach to the analysis of curvature square operators, understood as composites operators, which allows for the determination of the spectrum of scaling operators at the scale -invariant fixed point. The analysis suggests that there is one operator that becomes relevant close to d = 4 dimensions, while other operators previously found in the literature are either marginal or trivial on shell
A different kind of four dimensional brane for string theory
Full text linkWe present a generalization of the string's Polyakov action that describes a
conformally invariant four dimensional brane. The new extended object is very
different from the traditional D-branes of string theory, but, nevertheless,
shares some structural similarities with the string, especially when it comes
to the low-energy limit of small tension. We introduce a rather rich structure
of tensors that can play a role at low energies. In analogy with the bosonic
string, we initiate the quantization of the new brane discussing the extent in
which it produces a critical dimension of spacetime and Einstein's equations
coupled to a scalar dilaton under some approximations.Comment: 13 pages, v2: several improvements including a new section, to appear
in PR
Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories
No full textEnergy momentum tensors of higher-derivative free scalar conformal field
theories in flat spacetime are discussed. Two algorithms for the computation of
energy momentum tensors are described, which accomplish different goals: the
first is brute-force and highlights the complexity of the energy momentum
tensors, while the second displays some features of their geometric origin as
variations of Weyl invariant curved-space actions. New compact expressions for
energy momentum tensors are given and specific obstructions to defining them as
conformal primary operators in some spacetime dimensions are highlighted. Our
discussion is also extended to higher-derivative free spinor theories, which
are based on higher-derivative generalizations of the Dirac action and provide
interesting examples of conformal field theories in dimension higher than two.Comment: 29 pages, 2 tables; v2: new section on unitarity of 2- and 3-pf; v3:
further clarifications, to appear in JHE
Scale and conformal invariance in higher derivative shift symmetric theories
Full text linkThe critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical dimensions and studied at the leading non trivial order in perturbation theory. For two infinite families, one with quartic and one with cubic interactions, beta functions, criticality conditions and universal anomalous dimensions are computed. At the order considered, the cubic theories enjoy a one loop non renormalization of the vertex, so that the beta function depends non trivially only on the anomalous dimension. The trace of the energy momentum tensor is also investigated and it is shown that these two families of QFTs are conformally invariant at the fixed point of the RG flow
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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