Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice | Zendy

Daisuke Kadoh | Zendy; Yoshio Kikukawa | Zendy; Yoichi Nakayama | Zendy

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Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

Author(s) -

Daisuke Kadoh,

Yoshio Kikukawa,

Yoichi Nakayama

Publication year - 2004

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2004/12/006

Subject(s) - lattice gauge theory , lattice field theory , gauge anomaly , gauge theory , hamiltonian lattice gauge theory , physics , abelian group , cohomology , theoretical physics , lattice (music) , mathematics , mathematical physics , pure mathematics , acoustics

In the gauge-invariant construction of abelian chiral gauge theories on thelattice based on the Ginsparg-Wilson relation, the gauge anomaly is topologicaland its cohomologically trivial part plays the role of the local counter term.We give a prescription to solve the local cohomology problem within a finitelattice by reformulating the Poincar\'e lemma so that it holds true on thefinite lattice up to exponentially small corrections. We then argue that thepath-integral measure of Weyl fermions can be constructed directly from thequantities defined on the finite lattice.Comment: revised version, 35pages, using JHEP3.cl

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