Abstract
We construct supersymmetric Lifshitz field theories with four real supercharges in a general number of space dimensions. The theories consist of complex bosons and fermions and exhibit a holomorphic structure and non-renormalization properties of the superpotential. We study the theories in a diverse number of space dimensions and for various choices of marginal interactions. We show that there are lines of quantum critical points with an exact Lifshitz scale invariance and a dynamical critical exponent that depends on the coupling constants.
Highlights
Where d is the number of space dimensions and z is the dynamical critical exponent
In this work we studied the consequences of holomorphic time domain supersymmetry in the context of Lifshitz quantum field theories
We constructed a family of such models possessing four real supercharges which satisfy supersymmetric commutation relations closing on the Hamiltonian, endowing these systems with a holomorphic structure
Summary
Various types of non-relativistic supersymmetric field theories have been considered in the past from different motivations and points of view (see for example [13,14,15,16,17,18,19,20,21,22]). Depending on the Lifshitz dimension of these deformations, such theories have been shown to be perturbatively renormalizable (see [22, 29, 30], as well as the discussion in subsection 3.1) Note, that such interactions will generally break the Galilean invariance of the fermionic sector of the free model (with z = 2). Note that, while these interaction terms are invariant under the SU(2) R-symmetry, they generally break the fermionic Galilean symmetry of the free theory, as well as the U(1) and U(1)M symmetries (of the bosonic and fermionic sectors respectively) listed in table 1. In order to obtain a spontaneous breaking of supersymmetry on this level, one would have to consider a model with multiple interacting holomorphic superfields (as in the O’Raifeartaigh model)
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