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Register a new userGravity from Breaking of Local Lorentz Symmetry
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Authors
Robertus Potting
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We present a model of gravity based on spontaneous Lorentz symmetry breaking. We start from a model with spontaneously broken symmetries for a massless 2-tensor with a linear kinetic term and a nonderivative potential, which is shown to be equivalent to linearized general relativity, with the Nambu-Goldstone (NG) bosons playing the role of the gravitons. We apply a bootstrap procedure to the model based on the principle of consistent coupling to the total energy energy-momentum tensor. Demanding consistent application of the bootstrap to the potential term severely restricts the form of the latter. Nevertheless, suitable potentials exists that permit stable vacua. It is shown that the resulting model is equivalent, at low energy, to General Relativity in a fixed gauge.
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Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and diffeomorphism invariants. In particular, all the kinetic terms are prohibited except for spinor fields, and hence the other fields are auxiliary. Their kinetic terms, including those of the LL gauge field and the vierbein, are induced by spinor loops simultaneously with the LL gauge field mass. The LL symmetry is necessarily broken spontaneously and hence is nothing but a hidden local symmetry, from which gravity is emergent.
We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight difference between gravitons and photons from a common source could be measured.
We study nonlinear vacuum electrodynamics in a first-order formulation proposed by Plebanski. By applying a Dirac constraint analysis, we derive an effective Hamiltonian, together with the equations of motion. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing stationary points in which the field strength acquires a nonzero vacuum expectation value. The associated spontaneous breaking of Lorentz symmetry can in principle be detected by coupling the model to a suitable external current, or to gravity. We show that the possible vacua can be classified in four classes. We study some of their properties, using explicit examples for illustration.
We study the spontaneous Lorentz symmetry breaking in a field theoretical model in (2+1)-dimension, inspired by string theory. This model is a gauge theory of an anti-symmetric tensor field and a vector field (photon). The Nambu-Goldstone (NG) boson for the spontaneous Lorentz symmetry breaking is identified with the unphysical massless photon in the covariant quantization. We also discuss an analogue of the equivalence theorem between the amplitudes for emission or absorption of the physical massive anti-symmetric tensor field and those of the unphysical massless photon. The low-energy effective action of the NG-boson is also discussed.
We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z boson of the so-called mirror matter models.
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