Renormalization of Lorentz violating theories

Abstract

We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not generated by renormalization. Renormalizability is ensured by a "weighted power-counting" criterion. The theories contain a dimensionful parameter Lambda(L), yet a set of models are classically invariant under a weighted scale transformation, which is anomalous at the quantum level. Formulas for the weighted trace anomaly are derived. The renormalization-group properties are studied

Lorentz violation, gravity, dissipation and holography

“…Lorentz violation in QFT was revisited in [38,39]. The key point was that an UV scale invariant QFT with Lifshitz scaling symmetry has a different power counting structure, controlled by the dynamical exponent z.…”

Weighted power counting and perturbative unitarity

“…For the argument that there are no more than two time derivatives, and in particular no time derivatives in interactions with N > 2, the reader may check Ref. [3]. The weighted degree of divergence of the (…”

“…A more complete story of scalars and fermions can be found in Ref. [3], and for a more detailed discussion of gauge fields, see Refs. [8,9].…”

“…The idea of breaking Lorentz invariance by imposing Lifshitz-point scaling opened the doors to rendering previously nonrenormalizable theories renormalizable [3]. The main incentive is to obtain an UV (albeit Lorentz violating) completion of a nonrenormalizable field theory which becomes Lorentz invariant in the infrared.…”

“…Most recently, Lifshitz-point field theories have gained popularity because of the prospect of producing a consistent, renormalizable quantum theory of gravity [3,7]. A Lifshitz point is a conformal fixed point invariant under anisotropic rescalings of space and time, with suitable scaling dimensions for fields.…”