Talk presented by Hideo Nakajima

Parallel Session: Confinement III

Thursday July 1st, 14.50 - 15.10, Fermi Room

Authors: Hideo Nakajima and Sadataka Furui

Test of the Kugo-Ojima confinement criterion in the lattice Landau gauge

Abstract: We present the first results of test of the Kugo-Ojima confinement criterion in the lattice Landau gauge. The Kugo-Ojima criterion of color confinement in the BRS formulation of the continuum gauge theory is given by $u^a_b(0)=-delta^a_b$, where [int dx ^{ip(x-y)}langle 0|TD_mu c^a(x)g(A_nutimes bar c)^b(y)|0rangle (g_{mu nu}-{p_mu p_nu over p^2})u^a_b(p^2),] while the rigorous foundation of the BRS formulation of the lattice gauge theory is still an open problem though. We measured the lattice version of $u^a_b(0)$ in use of 1/(-partial D(A))$ where $D_mu(A)$ is a lattice covariant derivative in the new definition of the gauge field as $U=e^A$. We obtained that $u^a_b(0)$ is consistent with $-cdelta^a_b, c=0.67$ in quench simulation, $beta =5.5$, on $8^4$. We report the $beta$ dependence and the lattice size dependence of $c$.

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