Gravity, Lorentz violation, and the standard model

Abstract

The role of the gravitational sector in the Lorentz-and CPT-violating standard-model extension ͑SME͒ is studied. A framework is developed for addressing this topic in the context of Riemann-Cartan spacetimes, which include as limiting cases the usual Riemann and Minkowski geometries. The methodology is first illustrated in the context of the QED extension in a Riemann-Cartan background. The full SME in this background is then considered, and the leading-order terms in the SME action involving operators of mass dimension three and four are constructed. The incorporation of arbitrary Lorentz and CPT violation into general relativity and other theories of gravity based on Riemann-Cartan geometries is discussed. The dominant terms in the effective low-energy action for the gravitational sector are provided, thereby completing the formulation of the leading-order terms in the SME with gravity. Explicit Lorentz symmetry breaking is found to be incompatible with generic Riemann-Cartan geometries, but spontaneous Lorentz breaking evades this difficulty.

Lorentz violation, gravity, dissipation and holography

“…differ from [73,74] but are in accordance with reference [71,72] that shares many common points with the discussion of this section.…”

“…Couplings of Lorentz violating theories to gravity were considered before, [71][72][73][74]. Our conclusions…”

Global three-parameter model for neutrino oscillations using Lorentz violation

“…These oscillation effects are controlled by coefficients for Lorentz violation forming various 3 3 matrices denoted a L ab , c L ab , etc., where , are Lorentz indices and the matrix indices a, b label neutrino flavor and span e, , . It is elegant to regard these coefficients as arising from spontaneous Lorentz violation [19], which is consistent with Riemann geometry [5] and may be ubiquitous in effective field theories [20]. Some of the neutrino coefficients for Lorentz violation act to mimic aspects of conventional mass-induced oscillations, while others predict qualitatively new features of oscillations such as sidereal variations, direction dependence, unconventional spectral behavior, Lorentz-violating seesaws, neutrino-antineutrino mixing, and more.…”

“…Extending the GRcoupled SM by adding all terms that involve operators for Lorentz violation and that are scalars under coordinate transformations results in a general effective field theory called the Standard-Model Extension (SME). The leading terms in this theory include those of the SM and GR, together with ones violating Lorentz and CPT symmetry constructed from SM and GR fields [4,5].…”

Dynamical Chern–Simons modified gravity, Gödel Universe and variable cosmological constant

“…Among a great number of possible Lorentz-CPT breaking modification of gravity [1], the four-dimensional gravitational Chern-Simons term originally introduced in [2] is certainly the most popular one. The main reasons for it are its relatively simple form, evident gauge symmetry and straightforward analogies with the three-dimensional gravitational ChernSimons term [3].…”