1,721,000 research outputs found
Ultraviolet finite resummation of perturbative quantum gravity
No full textIf the metric is chosen to depend exponentially on the conformal factor, and if one works in a gauge where the conformal factor has the wrong sign propagator, perturbative quantum gravity corrections can be partially resummed into a series of terms each of which is ultraviolet finite. These new terms however are not perturbative in some small parameter, and are not individually BRST invariant, or background diffeomorphism invariant. With appropriate parametrisation, the finiteness property holds true also for a full phenomenologically relevant theory of quantum gravity coupled to (beyond the standard model) matter fields, provided massive tadpole corrections are set to zero by a trivial renormalisation
Quantum gravity, renormalizability and diffeomorphism invariance
No full textWe show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space L of renormalizable interactions, non-perturbative in ℏ, and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside L, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings. However by taking a limit to the boundary of L, the couplings can be constrained to recover Newton's constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed
Superluminal velocity through near-maximal neutrino oscillations or by being off shell
No full textRecently it was suggested that the observation of superluminal neutrinos by the OPERA collaboration may be due to group velocity effects resulting from close-to-maximal oscillation between neutrino mass eigenstates, in analogy to known effects in optics. We show that superluminal propagation does occur through this effect for a series of very narrow energy ranges, but this phenomenon cannot explain the OPERA measurement. Superluminal propagation can also occur if one of the neutrino masses is extremely small. However the effect only has appreciable amplitude at energies of order this mass and thus has negligible overlap with the multi-GeV scale of the experiment
Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity
No full textThe Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. Generically for the conformal sector, complete flows exist only in the reverse direction (i.e. from the infrared to the ultraviolet). The Gaussian fixed point supports infinite sequences of composite eigenoperators of increasing infrared relevancy (increasingly negative mass dimension), which are orthonormal and complete for bare interactions that are square integrable under the appropriate measure. These eigenoperators are non-perturbative in h and evanescent. For R4 spacetime, each renormalized physical operator exists but only has support at vanishing field amplitude. In the generic case of infinitely many non-vanishing couplings, if a complete RG flow exists, it is characterised in the infrared by a scale Λp > 0, beyond which the field amplitude is exponentially suppressed. On other spacetimes, of length scale L, the flow ceases to exist once a certain universal measure of inhomogeneity exceeds O(1) + 2πL2Λ2p . Importantly for cosmology, the minimum size of the universe is thus tied to the degree of inhomogeneity, with spacetimes of vanishing size being required to be almost homogeneous. We initiate a study of this exotic quantum field theory at the interacting level, and discuss what the full theory of quantum gravity should look like, one which must thus be perturbatively renormalizable in Newton’s constant but non-perturbative in h.<br/
Equivalence of local potential approximations
No full textIn recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents and Wilson-Fisher fixed points in three dimensions, providing a certain "optimised" cutoff is used for the Legendre flow equation. Here we point out that this is a consequence of an exact map between the two equations, which is nothing other than the exact reduction of the functional map that exists between the two exact renormalization groups. We note also that the optimised cutoff does not allow a derivative expansion beyond second order
The continuum limit of the conformal sector at second order in perturbation theory
No full textRecently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial σ is dressed with a coefficient function fσ Λ(ϕ) of the conformal factor field, ϕ. Each coefficient function is parametrised by an infinite number of underlying couplings, and decays at large ϕ with a characteristic amplitude suppression scale which can be chosen to be at a common value, Λp. Although the theory is perturbative in couplings it is non-perturbative in ~. At second order in perturbation theory, one must sum over all melonic Feynman diagrams to obtain the particular integral. We show that it leads to a well defined renormalized trajectory and thus continuum limit, provided it is solved by starting at an arbitrary cutoff scale Λ = µ which lies in the range 0 < µ < aΛp (a some non-universal number). If µ lies above this range the resulting coefficient functions become singular, and the flow ceases to exist, before the physical limit is reached. To this one must add a well-behaved complementary solution, containing irrelevant couplings determined uniquely by the first-order interactions, and renormalized relevant couplings. Even though some irrelevant couplings diverge in the limit Λp→∞, domains for the underlying relevant couplings can be chosen such that diffeomorphism invariance will be recovered in this limit, and where the underlying couplings disappear to be replaced by effective diffeomorphism invariant couplings
Conformal anomaly from gauge fields without gauge fixing
No full textWe show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularization is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken U(1|1) supergauge theory. We first provide a realization that leaves behind two versions of the original U(1) gauge field, and then construct a manifestly U(1|1) supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.</p
The functional f(R) approximation
No full textThis article is a review of functional approximations in the asymptotic safety approach to quantum gravity. It mostly focusses on a formulation that uses a non-adaptive cutoff, resulting in a second order differential equation. This formulation is used as an example to give a detailed explanation for how asymptotic analysis and Sturm-Liouville analysis can be used to uncover some of its most important properties. In particular, if defined appropriately for all values $-\inft
The canonical transformation and massive CSW vertices for MHV-SQCD
No full textThe similarity of massive CSW scalar vertices and quark vertices can be understood using a kind of light-cone SUSY transformation presented in this paper. We also show that the canonical transformation generating the MHV-SQCD Lagrangian, can be fixed by applying this light-cone SUSY transformation to the canonical transformation for MHV-QCD obtained in paper arxiv:0805.0239. Most of the massive CSW vertices for SQCD can also be pinned down in this way
Renormalizable extra-dimensional models
No full textNon-Abelian gauge theories may have continuum limits in more than four dimensions, supported by non-trivial ultra-violet fixed points. Moreover, such theories can be expected to be accessible to Wilson's epsilon expansion. We investigate this series for SU(N) Yang-Mills, in particular for the fixed point coupling and critical exponent nu, up to four loops. From the model-building point of view, such theories would be effectively perturbatively renormalizable in the normal way. A particularly attractive possibility is the construction of renormalizable extra-dimensional models of the weak interactions, which have the potential to address the full hierarchy problem. The simplest such gauge-Higgs unification model is however ruled out by a combination of theoretical and phenomenological constraints
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