Spontaneous breaking of Lorentz invariance

Abstract

We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving a non-zero fermion number density to the vacuum (and therefore dynamically generating a chemical potential term). This mechanism yields a finite vacuum expectation value ψ γ µ ψ , which we consider in the context of proposed models that require such a breaking of Lorentz invariance in order to yield composite degrees of freedom that act approximately like gauge bosons. We also make general remarks about how the background source provided by ψ γ µ ψ could relate to work on signals of Lorentz violation in electrodynamics.

Photon and photino as Nambu–Goldstone zero modes in an emergent SUSY QED

“…10 However, this sum rule is acceptably relaxed when taking into account large radiative corrections to the masses of the supersymmetric particles, which, according to the proposal, stem from the hidden sector. This is just what one may expect in conventional supersymmetric theories with the standard two-sector paradigm, according to which SUSY breaking entirely occurs in a hidden sector; then this spontaneous breaking is mediated to the visible sector by some indirect interactions whose nature depends on a particular mediation scenario [37][38][39].…”

“…In essence, we try to extend to their supersymmetric analogs the emergent gauge theories with SLIV and the associated emergence of gauge bosons as massless vector Nambu-Goldstone modes studied earlier [6][7][8][9][10][11][12] (see also [24][25][26][27][28]). Generally speaking, it may turn out that SLIV is not the only reason why massless photons could dynamically appear, if spacetime symmetry is further enlarged.…”

“…This old idea [3][4][5], supported by a close analogy with the dynamical origin of massless particle excitations for spontaneously broken internal symmetries, has gained new impetus in recent years. On the other hand, besides its generic implication for the possible origin of physical gauge fields [6][7][8][9][10][11][12] in a conventional quantum field theory (QFT) framework, there are many different contexts in the literature where Lorentz violation may stem itself from string theory [13,14], quantum gravity [15] or any unspecified dynamics at an ultraviolet scale perhaps related to the Planck scale [16][17][18][19][20][21][22]. Though we are mainly focused on the spontaneous Lorentz violation in QFT, particularly in QED and the Standard Model, we give below some brief comments on other approaches and we make clearer the aims and results of the present work.…”

Models of baryogenesis via spontaneous Lorentz violation

“…The vector A µ is not necessarily the field that is varied to get the equations of motion from this action; it could be the derivative of a scalar field ∂ µ φ [8,9,10,11,12,13,26], the vector current of some hidden fermionsψγ µ ψ [42,21,22,23,24], the four-divergence of some higher-rank tensor background field ∇ µ ∇ ν . .…”

“…In recent years there has been considerable interest in this possibility in the context of various quantum field theories, extra dimensions and brane-world scenarios as well as modified gravity and string theories [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]. The existence of Lorentz violation leads to interesting implications for neutrino experiments [31], high energy cosmic ray phenomena [16,32,33], evolution of the finestructure constant [34,35] and Newton's constant [36], the cosmological constant problem [37,38], dark energy [26,35,39], inflation [40], and the cosmic microwave background (CMB) [41].…”