Lifshitz fermionic theories with z=2 anisotropic scaling

Abstract

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.

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References in corpus (7)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Topological Order and Conformal Quantum Critical Points
• Renormalization of Lorentz violating theories
• Relating Field Theories via Stochastic Quantization

Cited by in corpus (10)

• The Most General Form of Deformation of the Heisenberg Algebra from the Generalized Uncertainty Principle
• Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories
• Dualities and bosonization of massless fermions in three dimensional space-time
• Discreteness of time in the evolution of the universe
• Entanglement Entropy with Lifshitz Fermions
• Asymptotically free lattice gauge theory in five dimensions
• Non-Local Deformation of a Supersymmetric Field Theory
• Entanglement in Lifshitz Fermion Theories
• Vacuum Radiation in $z=2$ Lifshitz QED
• Singularities of the Casimir Energy for Quantum Field Theories with Lifshitz Dimensions