We study a flavor-violating four-fermion interaction in the Lifshitz context, in 3 þ 1 dimensions and with a critical exponent z ¼ 3. This model is renormalizable, and features dynamical mass generation, as well as asymptotic freedom. At one-loop, it is only logarithmically divergent, but the superficial degree of divergence of the two-point functions is 3. We calculate the two-loop corrections to the propagators, and show that, at this order, the Lorentz-violating corrections to the IR dispersion relation are quadratic in the cut off. Furthermore, these corrections are too significant to represent a physical effect. As a consequence, the predictive power of the model in terms of Lorentz-violating effects in the propagation of particles is limited.

We study consequences of Lorentz symmetry violation in a z = 2 Lifshitz extension of QED in 3+1 dimensions, and we discuss non-trivial effects of quantization. Because of the specific power of space momentum in propagators of the model, dimensional regularization leads to an unusual interpretation of loop integrals, which are finite even when the space dimension goes to the integer 3. We check the consistency of the approach by calculating the (vanishing) corrections to the photon mass and the IR-divergence-free corrections to the dispersion relation for massless fermions.

It is known in previous literature that if a Wess-Zumino model with an R-symmetry gives a supersymmetric vacuum, the superpotential vanishes at the vacuum. In this work, we establish a formal notion of genericity, and show that if the R-symmetric superpotential has generic coefficients, the superpotential vanishes term-by-term at a supersymmetric vacuum. This result constrains the form of the superpotential which leads to a supersymmetric vacuum. It may contribute to a refined classification of R-symmetric Wess-Zumino models, and find applications in string constructions of vacua with small superpotentials. A similar result for a scalar potential system with a scaling symmetry is discussed.

We study how quantum fluctuations of the metric in covariant Hořava-Lifshitz gravity influence the propagation of classical fields (complex scalar and photon). The effective Lorentz-symmetry violation induced by the breaking of 4-dimensional diffeomorphism is then evaluated, by comparing the dressed dispersion relations for both external fields. The constraint of vanishing 3-dimensional Ricci scalar is imposed in the path integral, which therefore explicitly depends on two propagating gravitational degrees of freedom only. Because the matter fields are classical, the present model contains only logarithmic divergences. Furthermore, it imposes the characteristic Hořava-Lifshitz scale to be smaller than 10 10 GeV, if one wishes not to violate the current bounds on Lorentz symmetry violation.

No abstract