2 v 1 9 N ov 2 00 0 QCD 3 and the Replica Method
نویسندگان
چکیده
Using the replica method, we analyze the mass dependence of the QCD 3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fields. Three complementary approaches are considered in this article. First, we derive exact relations between the QCD 3 partition function and the QCD 4 partition function continued to half-integer topological charge. The replica limit of these formulas results in exact relations between the corresponding microscopic spectral densities of QCD 3 and QCD 4. Replica calculations, which are exact for QCD 4 at half-integer topological charge, thus result in exact expressions for the microscopic spectral density of the QCD 3 Dirac operator. Second, we derive Virasoro constraints for the QCD 3 partition function. They uniquely determine the small-mass expansion of the partition function and the corresponding sum rules for inverse Dirac eigenvalues. Due to de Wit-'t Hooft poles, the replica limit only reproduces the small mass expansion of the resolvent up to a finite number of terms. Third, the large mass expansion of the resolvent is obtained from the replica limit of a loop expansion of the QCD 3 partition function. Because of Duistermaat-Heckman localization exact results are obtained for the microscopic spectral density in this way.
منابع مشابه
ar X iv : h ep - l at / 0 01 10 26 v 2 1 3 N ov 2 00 0 1 QCD vacuum structure
Several issues related to the structure of the QCD vacuum are reviewed. We concentrate mostly on results concerning instantons and center vortices.
متن کاملar X iv : h ep - l at / 0 01 10 26 v 1 3 N ov 2 00 0 1 QCD vacuum structure
Several issues related to the structure of the QCD vacuum are reviewed. We concentrate mostly on results concerning instantons and center vortices.
متن کاملX iv : n uc l - th / 0 11 10 82 v 1 2 9 N ov 2 00 1 Lattice Study of the High Density State of SU ( 2 ) - QCD
We investigate high density state of SU(2) QCD by using Lattice QCD simulation with Wilson fermions. The ratio of fermion determinants is evaluated at each step of the Metropolis link update by Woodbury formula. At β = 0.7, and κ = 0.150, we calculate the baryon number density, the Polyakov lines, and the energy density of gluon sector with chemical potential μ=0 to 0.8 on the 43 × 12 lattice. ...
متن کاملar X iv : h ep - p h / 02 11 13 0 v 1 9 N ov 2 00 2 1 Twist - 3 effects for polarized virtual photon structure function
We investigate twist-3 effects in the polarized virtual photon. The structure function g γ 2 , which exists only for the virtual photon target and can be measured in future polarized e + e − collider experiments, receives both twist-2 and twist-3 contributions. The twist-3 part is analyzed in pure QED interaction as well as in LO QCD. We find the twist-3 contribution is appreciable for the phot...
متن کامل