Abstract
In previous works, we have proposed a new formulation of Yang-Mills theory on the lattice so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. This framework improves the Abelian projection in the gauge-independent manner. For quarks in the fundamental representation, we have demonstrated some numerical evidences for the restricted field dominance in the string tension, which means that the string tension extracted from the restricted part of the Wilson loop reproduces the string tension extracted from the original Wilson loop. However, it is known that the restricted field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation. In this paper, therefore, we focus on confinement of quarks in higher representations. By virtue of the non-Abelian Stokes theorem for the Wilson loop operator, we propose suitable gauge-invariant operators constructed from the restricted field to reproduce the correct behavior of the original Wilson loop averages for higher representations. Moreover, we perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators. We find that the proposed operators well reproduce the behavior of the original Wilson loop average, namely, the linear part of the static potential with the correct value of the string tension, which overcomes the problem that occurs in naively applying Abelian-projection to the Wilson loop operator for higher representations.
Highlights
The dual superconductor picture is one of the most promising scenarios for quark confinement [1]
While the main advantage of the field decomposition is its gauge covariance, another advantage is that, through a version of the non-Abelian Stokes theorem (NAST) invented originally by Diakonov and Petrov [15,16] and extended in a unified way in [17,18,19,20,21,22,23], the restricted field naturally appears in the surface-integral representation of the Wilson loop
We have developed the lattice version [28,29,30,31,32,33] of the reformulated Yang-Mills theory written in terms of new variables obtained by the gauge-covariant field decomposition, which enables us to perform the numerical simulations on the lattice in such a way that both the local gauge symmetry and the global color symmetry remain intact, in sharp contrast to the Abelian projection, which breaks both symmetries
Summary
The dual superconductor picture is one of the most promising scenarios for quark confinement [1]. While the main advantage of the field decomposition is its gauge covariance, another advantage is that, through a version of the non-Abelian Stokes theorem (NAST) invented originally by Diakonov and Petrov [15,16] and extended in a unified way in [17,18,19,20,21,22,23], the restricted field naturally appears in the surface-integral representation of the Wilson loop By virtue of this method, we understand how monopoles contribute to the Wilson loop at least classically.
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