The Planar Thirring Model with Kähler-Dirac Fermions

Abstract

Kähler's geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U($N)\otimes$U($N)$ field transformations, and has a parity-invariant mass term, both symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation-group fixed point are discussed.

arXiv commentcontribution to Symmetry special issue "New Applications of Symmetry to Lattice Field Theory"

References in corpus (11)

• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Critical Flavor Number in the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for Small N_f
• Kähler-Dirac fermions on Euclidean dynamical triangulations
• Critical flavour number of the Thirring model in three dimensions
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Topological fermion condensates from anomalies
• Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Topology and strong four fermion interactions in four dimensions

Cited by in corpus (5)

• Anomalies and symmetric mass generation for Kaehler-Dirac fermions
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Induced topological gravity and anomaly inflow from Kaehler-Dirac fermions in odd dimensions
• Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions