On the difference between Poincaré and Lorentz gravity

The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy–momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before.     

Spin–gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin–gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin–gravity coupling plays in particular problems.     

Discrete Painlevé equations and their appearance in quantum gravity

We discuss an algorithmic approach for both deriving discrete analogues of Painlevé equations as well as using such equations to characterize similarity reductions of spatially discrete integrable evolution equations. As a concrete example we show that a discrete analogue of Painlevé I can be used to characterize similarity solutions of the Kac-Moerbeke equation. It turns out that these similarity solutions also satisfy a special case of Painlevé IV equation. In addition we discuss a methodology for obtaining the relevant continuous limits not only at the level of equations but also at the level of solutions. As an example we use the WKB method in the presence of two turning points of the third order to parametrize (at the continuous limit) the solution of Painlevé I in terms of the solution of discrete Painlevé I. Finally we show that these results are useful for investigating the partition function of the matrix model in 2D quantum gravity associated with the measure exp [–t ₁ z ² –t ₂ z ⁴ –t ₃ z ⁶].     

Gauge invariance and the CPT and Lorentz violating induced Chern–Simons-like term in extended QED

The radiative induction of the CPT and Lorentz violating Chern–Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector b _μ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by quantum corrections. As a complement we obtain the result that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.     

The phase and critical point of quantum Einstein–Cartan gravity

By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S. Xue, Phys. Rev. D 82 (2010) 064039] the quantum Einstein–Cartan gravity in the framework of Regge calculus. On the basis of strong coupling expansion, mean-field approximation and dynamical equations satisfied by holonomy fields, we present in this Letter calculations and discussions to show the phase structure of the quantum Einstein–Cartan gravity, (i) the order phase: long-range condensations of holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range fluctuations of holonomy fields in weak gauge couplings. According to the competition of the activation energy of holonomy fields and their entropy, we give a simple estimate of the possible ultra-violet critical point and correlation length for the second-order phase transition from the order phase to disorder one. At this critical point, we discuss whether the continuum field theory of quantum Einstein–Cartan gravity can be possibly approached when the macroscopic correlation length of holonomy field condensations is much larger than the Planck length.     

The rotating black hole in renormalizable quantum gravity: The three-dimensional Hořava gravity case

Recently Ho?ava proposed a renormalizable quantum gravity, without the ghost problem, by abandoning Einstein?s equal-footing treatment of space and time through the anisotropic scaling dimensions. Since then various interesting aspects, including the exact black hole solutions have been studied but no rotating   black hole solutions have been found yet, except some limiting cases. In order to fill the gap, I consider a simpler three-dimensional set-up with z=2$z=2$ and obtain the exact rotating black hole solution. This solution has a ring curvature singularity inside the outer horizon, like the four-dimensional Kerr black hole in Einstein gravity, as well as a curvature singularity at the origin. The usual mass bound works also here but in a modified form. Moreover, it is shown that the conventional first law of thermodynamics with the usual Hawking temperature and chemical potential does not work, which seems to be the genuine effect of Lorentz-violating gravity due to lack of the absolute horizon.     

Quantizing gravity and spacetime: Where do we stand ?

We review five possible solutions to the riddle posed by Quantum Gravity: (1) Gravity should stay as a classical theory (L. Rosenfeld); (2) Quantum Gravity requires a formalism which will take the human mind (or the intelligent observer) into account, resolving at the same time the riddle of the collapse of the wave function/state vector in Quantum Mechanics in general (Penrose); (3) Perturbative Quantization; (4) Hamiltonian Quantization (Dirac, Ashtekar); (5) String Theory. We also discuss the quantization of spacetime.     

Holography beyond conformal invariance and AdS isometry?

Journal of Experimental and Theoretical Physics - We suggest that the principle of holographic duality be extended beyond conformal invariance and AdS isometry. Such an extension is based on a...     

High scale parity invariance as a solution to the SUSY CP problem and an explanation of small ε′/ε

It is shown that if the supersymmetric Standard Model (MSSM) emerges as the low energy limit of a high scale left-right symmetric gauge structure, the number of uncontrollable CP violating phases of MSSM are drastically reduced. In particular it guarantees the vanishing of the dangerous phases that were at the root of the so called SUSY CP problem. Such a symmetric gauge structure is independently motivated by the smallness of neutrino masses that arise via seesaw mechanism automatic in the theory. The minimal version of this theory also provides an explanation of the smallness of ε′/ε as a consequence of the high scale parity invariance. This talk is based on work done in collaboration with K S Babu and B Dutta.     

Is the quantum dot at large bias a weak-coupling problem?

We examine the two-lead Kondo model for a dc-biased quantum dot in the Coulomb blockade regime. From perturbative calculations of the magnetic susceptibility, we show that the problem retains its strong-coupling nature, even at bias voltages larger than the equilibrium Kondo temperature. We give a speculative discussion of the nature of the renormalization group flows and the strong-coupling state that emerges at large voltage bias.     

Can gravity distinguish between Dirac and Majorana neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and the gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavor system, as shown explicitly for SN 1987A.     

Primordial perturbations and non-gaussianities in Ho?ava-Lifshitz gravity

We investigate primordial perturbations and non-gaussianities in the Ho?ava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Ho?ava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are " slow-roll suppressed” in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on Ho?ava-Lifshitz gravity.