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arXiv · 2403.03420

Yet another lattice formulation of 2D $U(1)$ chiral gauge theory via bosonization

Okuto Morikawa·Soma Onoda·Hiroshi Suzuki
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Abstract

Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is \emph{exactly\/} preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose a yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the ``magnetic charge'' in the bosonization, is represented by a ``hole'' excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

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Okuto Morikawa, Soma Onoda, Hiroshi Suzuki. 2024-05-27. Yet another lattice formulation of 2D $U(1)$ chiral gauge theory via bosonization. https://arxiv.org/abs/2403.03420

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