arXiv subjects

Claudio Borquez

Publications and source records attributed to Claudio Borquez.

7 recordsLinked to original sources

arXiv2024

Renormalization of the nonprojectable Horava theory

We present the proof of renormalization of the Horava theory, in the nonprojectable version. We obtain a form of the quantum action that exhibits a manifest BRST-symmetry structure. Previous analysis has shown that the divergences produced by irregular loops cancel completely between them. The remaining divergences are local. The renormalization is achieved by using the approach developed by Barvinsky et al. with the background-field formalism.

hep-th↗

arXiv2023

Effective action of the Horava theory: Cancellation of divergences

We compute the one-loop effective action of the Horava theory, in its nonprojectable formulation. We take the quantization of the (2+1)-dimensional theory in the Batalin-Fradkin-Vilkovisky formalism, and comment on the extension to the (3+1) case. The second-class constraints and the appropriate gauge-fixing condition are included in the quantization. The ghost fields associated with the second-class constraints can be used to get the integrated form of the effective action, which has the form of a Berezinian. We show that all irregular loops cancel between them in the effective action. The key for the cancellation is the role of the ghosts associated with the second-class constraints. These ghosts form irregular loops that enter in the denominator of the Berezinian, eliminating the irregular loops of the bosonic nonghost sector. Irregular loops produce dangerous divergences; hence their cancellation is an essential step for the consistency of the theory. The cancellation of this kind of divergences is in agreement with the previous analysis done on the (2+1) quantum canonical Lagrangian and its Feynman diagrams.

hep-th↗

arXiv2023

Quantization of the anisotropic conformal Horava theory

We perform the Batalin-Fradkin-Vilkovisky quantization of the anisotropic conformal Horava theory in d spatial dimensions. We introduce a model with a conformal potential suitable for any dimension. We define an anisotropic and local gauge-fixing condition that accounts for the spatial diffeomorphisms and the anisotropic Weyl transformations. We show that the BRST transformations can be expressed mainly in terms of a spatial diffeomorphism along a ghost field plus a conformal transformation with another ghost field as argument. We study the quantum Lagrangian in the d=2 case, obtaining that all propagators are regular, except for the fields associated with the measure of the second-class constraints. This behavior is qualitatively equal to the nonconformal case.

hep-th↗

arXiv2022

BRST symmetry and unitarity of the Horava theory

We present an analysis on the BRST symmetry transformations of the Horava theory under the BFV quantization, both in the nonprojectable and projectable cases. We obtain that the BRST transformations are intimately related to a particular spatial diffeomorphism along one of the ghost vector fields. We show explicitly the invariance of the quantum action and the nilpotence of the BRST transformations, using this diffeomorphism largely. The BRST symmetry is verified in the whole phase space, inside and outside the constrained surface. When restricted to the constrained surface, the BRST transformations are completely local. The consistency of the BRST symmetry is a fundamental feature of a quantum field theory, specially for renormalization. The BFV quantization is independent of the chosen gauge-fixing condition. This allows us to show the unitarity of the quantum Horava theory, covering the gauge required for renormalization.

hep-th↗

arXiv2022

Cancellation of divergences in the nonprojectable Horava theory

We perform an analysis of the ultraviolet divergences of the quantum nonprojectable Horava gravity. We work the quantum field theory directly in the Hamiltonian formalism provided by the Batalin-Fradkin-Vilkovisky quantization. In this way the second-class constraints can be incorporated to the quantization. A known local gauge-fixing condition leads to a local canonical Lagrangian. Although the canonical fields acquire regular propagators, irregular propagators persist for the field associated to the measure of the second-class constraints. Loops can be formed with the irregular propagators producing potentially dangerous subdivergences. We show that all these loops cancel exactly between them due to a perfect matching between the propagators and vertices of the fields and ghosts forming the loops. The rest of divergences behaves similiarly to the projectable theory, they can be removed by local counterterms. This result points to the renormalization of the nonprojectable Horava theory.

hep-th↗

arXiv2021

Quantum Lagrangian of the Horava theory and its nonlocalities

We perform the BFV quantization of the 2+1 projectable and the 3+1 nonprojectable versions of the Horava theory. This is a Hamiltonian formalism, and noncanonical gauges can be used with it. In the projectable case, we show that the integration on canonical momenta reproduces the quantum Lagrangian known from the proof of renormalization of Barvinsky et al. This quantum Lagrangian is nonlocal, its nonlocality originally arose as a consequence of getting regular propagators. The matching of the BFV quantization with the quantum Lagrangian reinforces the program of quantization of the Horava theory. We introduce a local gauge-fixing condition, hence a local Hamiltonian, that leads to the nonlocality of the Lagrangian after the integration. For the case of the nonprojectable theory, this procedure allows us to obtain the complete (nonlocal) quantum Lagrangian that takes into account the second-class contraints. We compare with the integration in general relativity, making clear the relationship between the underlying anisotropic symmetry of the Horava theory and the nonlocality of its quantum Lagrangian.

hep-th↗

arXiv2020

Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory

We present the interesting case of the 2+1 nonprojectable Horava theory formulated at the critical point, where it does not posses local degrees of freedom. The critical point is defined by the value of a coupling constant of the theory. We discuss how, in spite of the absence of degrees of freedom, the theory admits solutions with nonflat or nonconstant curvature. We consider the theory without cosmological constant and without terms of higher order derivatives, hence this is an effect that can be seen at the same order of 2+1 general relativity. We present an exact nonflat solution that is not asymptotically flat. The presence of solutions with nontrivial curvature seems to be related to the relaxing of the asymptotically flat condition. We discuss that there is no analogue of Newtonian potential in this theory, and a broad class of asymptotically flat geometries leads to the restriction that the only solutions that can be found among them are the flat ones.

gr-qc↗