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Title Topological gauge actions on the lattice as Overlap fermion determinants
Authors Nikhil Sridharan Karthik,Rajamani Narayanan
JLAB number JLAB-THY-22-3591
LANL number arXiv:2203.16388
Other number DOE/OR/23177-5462
Document Type(s) (Journal Article) 
Associated with EIC: No
Supported by Jefferson Lab LDRD Funding: No
Funding Source: Nuclear Physics (NP)
Other Funding:DE-FG02- 04ER41302

Compiled for to be submitted to arXiv
Publication Abstract: Overlap fermion on the lattice has been shown to properly reproduce topological aspects of gauge fields. In this paper, we review the derivation of Overlap fermion formalism in a torus of three space-time dimensions. Using the formalism, we show how to use the Overlap fermion determinants in the massless and infinite mass limits to construct different continuum topological gauge actions, such as the level-k Chern-Simons action, 'half-CS' term and the BF coupling, in a gauge-invariant lattice UV regulated manner. Taking special Abelian and non-Abelian background fields, we demonstrate numerically how the lattice formalism beautifully reproduces the continuum expectations, such as the flow of action under large gauge transformations.
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