English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the lattice formulation of SO(10) chiral gauge theory withleft-handed Weyl fermions in the sixteen dimensional spinor representation($\underline{16}$) within the framework of the Overlap fermion/theGinsparg-Wilson relation. We define a manifestly gauge-invariant path-integralmeasure for the left-handed Weyl field using all the components of the Diracfield, but the right-handed part of which is just saturated completely byinserting a suitable product of the SO(10)-invariant 't Hooft vertices in termsof the right-handed field. The definition of the measure applies to allpossible topological sectors. The measure possesses all required transformationproperties under lattice symmetries and the induced effective action is CPinvariant. The global U(1) symmetry of the left-handed field is anomalous dueto the non-trivial transformation of the measure, while that of theright-handed field is explicitly broken by the 't Hooft vertices. There remainsthe issue of locality in the gauge-field dependence of the Weyl fermionmeasure, but the question can be addressed in the weak gauge-coupling expansionat least using Monte Carlo methods without encountering the sign problem. Wealso discuss the relations of our formulation to other approaches/proposals todecouple the species-doubling/mirror degrees of freedom. Those includeEichten-Preskill model, Ginsparg-Wilson Mirror-fermion model, Domain wallfermion model with the boundary Eichten-Preskill term, 4D TopologicalInsulator/Superconductor with gapped boundary phase, and the recent studies onthe PMS phase/"Mass without symmetry breaking". We clarify the similarity andthe difference in technical detail and show that our proposal is a well-definedtesting ground for that basic question.

On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)