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Register a new userAspects of the Bosonic Spectral Action
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Added by
Mairi Sakellariadou
Publication date
2015
fields
Physics
and research's language is
English
Authors
Mairi Sakellariadou
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A brief description of the elements of noncommutative spectral geometry as an approach to unification is presented. The physical implications of the doubling of the algebra are discussed. Some high energy phenomenological as well as various cosmological consequences are presented. A constraint in one of the three free parameters, namely the one related to the coupling constants at unification, is obtained, and the possible role of scalar fields is highlighted. A novel spectral action approach based upon zeta function regularisation, in order to address some of the issues of the traditional bosonic spectral action based on a cutoff function and a cutoff scale, is discussed.
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We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stuckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stuckelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field $A_mu$, the Faraday tensor $F_{mu u}$ and its Hodge dual $tilde{F}_{mu u}$.
One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for scalar curvature cosmological fluctuations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scale. This quantum tilt is imprinted, in a scale dependent energy uncertainty for the spectator modes. The effective quasi de Sitter description of this model independent energy uncertainty uniquely sets the effective quasi de Sitter parameters at all energy scales. In particular, in the slow-roll regime characterized by an almost constant $epsilon$, the quantum Fisher -- model independent -- prediction for the spectral index is $(1-n_s) = 0.0328$ ($n_s=0.9672$). Moreover, the energy scale dependence of the quantum cosmological tilt implies the existence of a cosmological phase transition at energies higher than the CMB scale where the tilt goes from red into blue. This strongly suggest the existence of a pre-inflationary phase where the effective scalaron contributes to the spectral index as normal relativistic matter and where the corresponding growth of the power spectrum can result in dark matter in the form of small mass primordial black holes. The source and features of the quantum cosmological tilt leading to these predictions are determined by the entanglement features of the de Sitter vacuum states.
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature.
The mean-square width of the energy profile of bosonic string is calculated considering two boundary terms in the effective action. The perturbative expansion of the Lorentz-invariant boundary terms at the second and the fourth order in the effective action is taken around the free Nambu-Goto action. The calculation are presented for open strings with Dirichlet boundary condition on cylinder.
We prove the renormalizability to all orders of a refined Gribov-Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the Faddeev-Popov operator is positive definite with respect to the transverse component of the gauge field, a procedure which turns out to be analogous to the restriction to the Gribov region in the Landau gauge. The model studied here can be regarded as the first approximation of a more general nonperturbative BRST invariant formulation of the refined Gribov-Zwanziger action in linear covariant gauges obtained recently in [Phys. Rev. D 92, no. 4, 045039 (2015) and arXiv:1605.02610 [hep-th]]. A key ingredient of the set up worked out in [Phys. Rev. D 92, no. 4, 045039 (2015) and arXiv:1605.02610 [hep-th]] is the introduction of a gauge invariant field configuration $mathbf{A}_{mu}$ which can be expressed as an infinite non-local series in the starting gauge field $A_mu$. In the present case, we consider the approximation in which only the first term of the series representing $mathbf{A}_{mu}$ is considered, corresponding to a pure transverse gauge field. The all order renormalizability of the resulting action gives thus a strong evidence of the renormalizability of the aforementioned more general nonperturbative BRST invariant formulation of the Gribov horizon in linear covariant gauges.
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