scholarly journals The two-dimensional twisted reduced principal chiral model revisited

2018 ◽  
Vol 2018 (6) ◽  
Author(s):  
Antonio González-Arroyo ◽  
Masanori Okawa
Keyword(s):  
Chiral Model ◽  
Two Dimensional ◽  
Principal Chiral Model

scholarly journals QUANTUM MECHANICALLY INDUCED WESS–ZUMINO TERM IN THE PRINCIPAL CHIRAL MODEL

1998 ◽  
Vol 13 (37) ◽  
pp. 3017-3024 ◽  
Author(s):  
HITOSHI MIYAZAKI ◽  
IZUMI TSUTSUI
Keyword(s):  
Configuration Space ◽  
Critical Value ◽  
Chiral Model ◽  
Quantum Level ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Dirac Monopole ◽  
Principal Chiral Model

It is argued that in the two-dimensional principal chiral model, the Wess–Zumino term may be induced quantum mechanically in a manner analogous to the θ-term in QCD. Our argument is based on the fact that the configuration space of the model has a structure topologically identified as a sphere, and that the Dirac monopole potential, which is induced on the sphere by inequivalent quantizations, appears in the guise of the Wess–Zumino term. Our result suggests that, at the critical value λ2=8π/|k| of the coupling constant, the principal chiral model belongs to the same family of models with the Wess–Zumino–Novikov–Witten model at the quantum level.

scholarly journals Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

2018 ◽  
Vol 175 ◽  
pp. 11007 ◽  
Author(s):  
Christof Gattringer ◽  
Daniel Göschl ◽  
Carlotta Marchis
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Space Time ◽  
Field Theories ◽  
Gauge Fields ◽  
Chiral Model ◽  
Staggered Fermions ◽  
Lattice Field ◽  
Principal Chiral Model ◽  
Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

Sign in / Sign up

Export Citation Format

Share Document