Supersymmetry and Lorentz violation

Abstract

Supersymmetric field theories can be constructed that violate Lorentz and CPT symmetry. We illustrate this with some simple examples related to the original Wess-Zumino model. DOI: 10.1103/PhysRevD.65.091701 PACS number͑s͒: 11.30.Pb, 11.30.Cp, 11.30.Er A major development in fundamental theoretical physics during the past century has been the understanding of the central role played by spacetime symmetries in nature. Conventional spacetime symmetries, including Lorentz and CPT invariance, are now deeply ingrained in modern theories such as the standard model of particle physics and general relativity. Recent research includes investigations of larger spacetime symmetries, notably supersymmetry ͓1͔, and of the possibility that small violations of conventional spacetime symmetry could arise in an underlying theory at the Planck scale ͓2͔.The essence of spacetime supersymmetry is the existence of transformations between bosons and fermions that yield a translation operator upon anticommutation:where the energy-momentum 4-vector P generates spacetime translations, the spinor Q generates supersymmetry transformations, and ␥ are the Dirac matrices. Many supersymmetric Lorentz-invariant models exist. However, if supersymmetry is relevant to nature, experiment suggests it must be broken. Much of the phenomenology of supersymmetry conducted today is therefore within the context of the ͑minimal͒ supersymmetric standard model ͓3͔ in which soft supersymmetry-breaking but Lorentz-preserving interactions are added by hand. Soft interactions are superrenormalizable, while nonrenormalizable terms are taken to be suppressed by powers of the Planck scale or some other large scale associated with new physics. Soft terms can be motivated by studies of more fundamental theories and could arise from spontaneous breaking of supersymmetry ͓4͔. Their physical implications at low energies can be analyzed in the framework of supersymmetric standard-model extensions including supersymmetry-breaking terms.In a related vein, the physical implications of the breaking of conventional spacetime symmetries can be investigated using a general standard-model extension ͓5͔. Its Lagrangian contains terms violating Lorentz and CPT symmetry. Like the supersymmetry-breaking effects described above, these terms could arise from spontaneous symmetry violation. The nonlocal character of string theories offers a potential source for these terms with a natural origin in spontaneous Lorentz breaking ͓6͔ and provides strong motivation for investigating their physical implications at low energy. The renormalizable sector of the standard-model extension is a local field theory that would dominate Lorentz-and CPT-violating effects in low-energy physics. The requisite causality or positivity issues that result from treating the nonlocal underlying theory as a local field theory emerge at a high-energy scale determined by the Planck mass ͓7͔.In this work, we consider an issue unaddressed in the literature: the existence of fully supersymmetric theories incorpo...

Lorentz violation bounds on Bhabha scattering

“…The interest in this issue appears in different contexts, such as supersymmetric models [5,6], noncommutative geometry [7], gravity and cosmology [8][9][10][11], high derivative models [12][13][14], renormalization [15][16][17][18] and scattering processes [19,20] in quantum electrodynamics (QED), condensed matter systems [21][22][23], and so on. Following these theoretical developments, many experimental tests on Lorentz-violating (LV) corrections have also been carried out and several constraints on LV parameters were established [24].…”

The Lorentz-Violating Extension of the Standard Model

“…We finally mention that the need for a low-energy description beyond effective field theory is also unlikely to arise in the context of candidate underlying models with novel Lorentz-invariant aspects, such as additional particles, new symmetries, or large extra dimensions. Lorentz-symmetric modifications can therefore be implemented into the SME, if necessary [85][86][87].…”

Remarks on the causality, unitarity and supersymmetric extension of the Lorentz and CPT-violating Maxwell-Chern-Simons model

“…The first proposal of a supersymmetry-preserving Lorentz violation was carried out in the work of Ref. [4]. The aim of that work was to investigate whether one could maintain desired properties of supersymmetric systems, namely, cancellation of divergences and the patterns of spontaneous breaking schemes, while violating Lorentz symmetry.…”

“…Working upon a modified Wess-Zumino model, the authors of Ref. [4] had demonstrated that convenient changes of the Susy-algebra of fermionic charges and of Susycovariant derivatives expressions were enough to define a Susy-like invariance for the Lorentz violating starting theory. As a matter of fact the modification of the algebra was achieved by adding a particular tensor-dependent central term, of the k µυ ∂ ν type, where k µυ exhibits real symmetric traceless tensor properties.…”

“…Eventually a common feature arises: the violation is implemented by keeping either a four-vector (in a CPT-odd term [1]) or a traceless symmetric tensor (CPT-preserving term [2]) unchanged by particle inertial frame transformations [3] which is generally called spontaneous violation. Furthermore, the issue of preserving supersymmetry (Susy) while violating Lorentz symmetry is addressed to [4]. This breaking of Lorentz symmetry is also phenomenologically motivated as a candidate to explain the patterns observed in the detection of ultra-high energy cosmic rays, concerning the events with energy above the GZK ( E GZK ≃ 4×10 19 eV.T ) cutoff [6].…”