Phase-diagram of two-color lattice QCD in the chiral limit

We study thermodynamics of strongly coupled lattice QCD with two colors of massless staggered fermions as a function of the baryon chemical potential $\mu$ in 3+1 dimensions using a new cluster algorithm. We find evidence that the model undergoes a weak first order phase transition at $\mu=0$ which becomes second order at a finite $\mu$. Symmetry considerations suggest that the universality class of these phase transitions should be governed by an $O(N)\times O(2)$ field theory with collinear order, with N=3 at $\mu=0$ and N=2 at $\mu \neq 0$. The universality class of the second order phase transition at $\mu\neq 0$ appears to be governed by the decoupled XY fixed point present in the $O(2)\times O(2)$ field theory. Finally we show that the quantum (T=0) phase transition as a function of $\mu$ is a second order mean field transition.Comment: 31 pages, 12 figure

Chiral Limit of Strongly Coupled Lattice Gauge Theories

We construct a new and efficient cluster algorithm for updating strongly coupled U(N) lattice gauge theories with staggered fermions in the chiral limit. The algorithm uses the constrained monomer-dimer representation of the theory and should also be of interest to researchers working on other models with similar constraints. Using the new algorithm we address questions related to the chiral limit of strongly coupled U(N) gauge theories beyond the mean field approximation. We show that the infinite volume chiral condensate is non-zero in three and four dimensions. However, on a square lattice of size $L$ we find $\sum_x \sim L^{2-\eta}$ for large $L$ where $\eta = 0.420(3)/N + 0.078(4)/N^2$. These results differ from an earlier conclusion obtained using a different algorithm. Here we argue that the earlier calculations were misleading due to uncontrolled autocorrelation times encountered by the previous algorithm.Comment: 36 Pages, 9 figures, aps revtex forma

Topological Phases in Neuberger-Dirac operator

The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V = D_w (D_w^{\dagger} D_w)^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-\eta}$ at large volumes with $0\leq\eta\leq 0.25$ for $0\leq T\leq T_c$.Comment: Revtex format; 4 pages, 2 figure

Role of the σ\sigma-resonance in determining the convergence of chiral perturbation theory

The dimensionless parameter $\xi = M_\pi^2/(16 \pi^2 F_\pi^2)$, where $F_\pi$ is the pion decay constant and $M_\pi$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $\sigma$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $\xi$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the $p$-regime and the $\epsilon$-regime as expected. However, $\xi \lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $\xi > 0.0035$ the data begin to deviate dramatically from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $\sigma$-resonance in our model. Our findings may be useful for lattice QCD studies.Comment: 5 pages, 6 figures, revtex forma

Anomalous Chiral Symmetry Breaking above the QCD Phase Transition

We study the anomalous breaking of U_A(1) symmetry just above the QCD phase transition for zero and two flavors of quarks, using a staggered fermion, lattice discretization. The properties of the QCD phase transition are expected to depend on the degree of U_A(1) symmetry breaking in the transition region. For the physical case of two flavors, we carry out extensive simulations on a 16^3 x 4 lattice, measuring a difference in susceptibilities which is sensitive to U_A(1) symmetry and which avoids many of the staggered fermion discretization difficulties. The results suggest that anomalous effects are at or below the 15% level.Comment: 10 pages including 2 figures and 1 tabl

Dirac eigenvalues and eigenvectors at finite temperature

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.Comment: Lattice 2000 (Finite Temperature), 5 page

Constraints and Period Relations in Bosonic Strings at Genus-g

We examine some of the implications of implementing the usual boundary conditions on the closed bosonic string in the hamiltonian framework. Using the KN formalism, it is shown that at the quantum level, the resulting constraints lead to relations among the periods of the basis 1-forms. These are compared with those of Riemanns' which arise from a different consideration.Comment: 16 pages, (Plain Tex), NUS/HEP/9320