On Lorentz-Violating Supersymmetric Quantum Field Theories

TL;DR

This paper investigates the construction of Lorentz-violating supersymmetric quantum field theories that are renormalizable, revealing strict restrictions and concluding that supersymmetry does not resolve the Lorentz fine-tuning problem.

Contribution

It demonstrates that renormalizability constraints severely limit Lorentz-violating supersymmetric theories, especially in gauge theories, and shows the incompatibility with solving the Lorentz fine-tuning problem.

Findings

Lorentz-violation and supersymmetry are compatible at high energies.

Renormalizability restricts Lorentz-violating operators to a non-renormalized parameter c.

Supersymmetric gauge theories require the weighted power counting to match the usual one.

Abstract

We study the possibility of constructing Lorentz-violating supersymmetric quantum field theories under the assumption that these theories have to be described by lagrangians which are renormalizable by weighted power counting. Our investigation starts from the observation that at high energies Lorentz-violation and the usual supersymmetry algebra are algebraically compatible. Demanding linearity of the supercharges we see that the requirement of renormalizability drastically restricts the set of possible Lorentz-violating supersymmetric theories. In particular, in the case of supersymmetric gauge theories the weighted power counting has to coincide with the usual one and the only Lorentz-violating operators are introduced by some weighted constant c that explicitly appears in the supersymmetry algebra. This parameter does not renormalize and has to be very close to the speed of light at low energies in order to satisfy the strict experimental bounds on Lorentz violation. The only possible models with non trivial Lorentz-violating operators involve neutral chiral superfields and do not have a gauge invariant extension. We conclude that, under the assumption that high-energy physics can be described by a renormalizable Lorentz-violating extensions of the Standard Model, the Lorentz fine tuning problem does not seem solvable by the requirement of supersymmetry.