Study of the chiral behavior of [the chiral condensate] in quenched QCD.pdfVIP

1 Study of the chiral behavior of in quenched QCD Adrian Kaehlera ∗ a Department of Physics, Columbia University, New York, NY 10027, USA 7 The QCD phase transition is studied on 323 ×8 quenched lattices. One expects from simple arguments that 9 the quenched chiral condensate should diverge as the chiral limit is approached. Previous studies have not been 9 able to observe this behavior, perhaps due to relatively large lattice spacings used. The topic is revisited here on 1 N = 8 lattices, where the physical spacing is approximately (2 GeV )−1. t p e S 1. INTRODUCTION 2. THEORY 9 2 Quenched QCD provides an interesting oppor- It is not difficult to show that the chiral conden- tunity to study the role of topological effects on sate is just the trace of the the Euclidean fermion 1 the axial U (1)A symmetry above the chiral sym- propagator (i D + m). By looking at this trace in v metry restoring phase transition. Because it will the representation of the eigenvectors of the Dirac 1 4 turn out that our results elucidate features of the operator itself, we can separate the contributions 1 full dynamical theory as well, they have bearing to the chiral condensate into two parts [2]: 9 on a wide class of problems, in particular the or- i D − m 1 2m 0 der of the QCD phase transition itself[1]. T r (D2 − m2 ) = Nzm × m + λ2 + m2 (1) 7 We will begin by reviewing the role of small