Topological susceptibility in two-flavor lattice QCD with exact chiral symmetry

Abstract

We determine the topological susceptibility $χ_t$ in two-flavor QCD using the lattice simulations at a fixed topological sector. The topological charge density is unambiguously defined on the lattice using the overlap-Dirac operator which possesses exact chiral symmetry. Simulations are performed on a $16^3 \times 32$ lattice at lattice spacing $\sim$ 0.12 fm at six sea quark masses $m_q$ ranging in $m_s/6$--$m_s$ with $m_s$ the physical strange quark mass. The $χ_t$ is extracted from the constant behavior of the time-correlation of flavor-singlet pseudo-scalar meson two-point function at large distances, which arises from the finite size effect due to the fixed topology. In the small $m_q$ regime, our result of $χ_t$ is proportional to $m_q$ as expected from chiral effective theory. Using the formula $χ_t=m_qΣ/N_f$ by Leutwyler-Smilga, we obtain the chiral condensate in $N_f=2$ QCD as $Σ^{\bar{\mathrm{MS}}}(\mathrm{2 GeV}) = [252(5)(10) \mathrm{MeV}]^3 $, in good agreement with our previous result obtained in the $ε$-regime.

11 pages, 3 figures, v2: accepted for publication in PLB