A solvable twisted one-plaquette model

We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the time-like link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the hamiltonian limit, and the related Douglas-Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, in agreement with previous results by Karsch.Comment: Minor corrections; final version to appear on IJMPA. 22 pages, Latex, 2 (small) figures included with eps

Analytic results in 2+1-dimensional Finite Temperature LGT

In a 2+1-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as $\beta_c(n_t) = J_c n_t + a_1$, where $n_t$ is the number of links in the ``time-like'' direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the space-like plaquettes, and we are able to compute analytically in this context the coefficient $a_1$ for any SU(N) gauge group; the value of $J_c$ is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the 2+1-dimensional theory, space-like plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.Comment: 15 pages, Latex, 2 figures included with eps

Two dimensional QCD is a one dimensional Kazakov-Migdal model

We calculate the partition functions of QCD in two dimensions on a cylinder and on a torus in the gauge $\partial_{0} A_{0} = 0$ by integrating explicitly over the non zero modes of the Fourier expansion in the periodic time variable. The result is a one dimensional Kazakov-Migdal matrix model with eigenvalues on a circle rather than on a line. We prove that our result coincides with the standard expansion in representations of the gauge group. This involves a non trivial modular transformation from an expansion in exponentials of $g^2$ to one in exponentials of $1/g^2$. Finally we argue that the states of the $U(N)$ or $SU(N)$ partition function can be interpreted as a gas of N free fermions, and the grand canonical partition function of such ensemble is given explicitly as an infinite product.Comment: DFTT 15/93, 17 pages, Latex (Besides minor changes and comments added we note that for U(N) odd and even N have to be treated separately

Effective actions for finite temperature Lattice Gauge Theories

We consider a lattice gauge theory at finite temperature in ($d$+1) dimensions with the Wilson action and different couplings $\beta_t$ and $\beta_s$ for timelike and spacelike plaquettes. By using the character expansion and Schwinger-Dyson type equations we construct, order by order in $\beta_s$, an effective action for the Polyakov loops which is exact to all orders in $\beta_t$. As an example we construct the first non-trivial order in $\beta_s$ for the (3+1) dimensional SU(2) model and use this effective action to extract the deconfinement temperature of the model.Comment: Talk presented at LATTICE96(finite temperature

Lattice supersymmetry in 1D with two supercharges

A consistent formulation of a fully supersymmetric theory on the lattice has been a long standing challenge. In recent years there has been a renewed interest on this problem with different approaches. At the basis of the formulation we present in the following there is the Dirac-Kahler twisting procedure, which was proposed in the continuum for a number of theories, including N=4 SUSY in four dimensions. Following the formalism developed in recent papers, an exact supersymmetric theory with two supercharges on a one dimensional lattice is realized using a matrix-based model. The matrix structure is obtained from the shift and clock matrices used in two dimensional non-commutative field theories. The matrix structure reproduces on a one dimensional lattice the expected modified Leibniz rule. Recent claims of inconsistency of the formalism are discussed and shown not to be relevant.Comment: 14 pages, Presented by SA and AD at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Quantum disordered phase in a doped antiferromagnet

A quantitative description of the transition to a quantum disordered phase in a doped antiferromagnet is obtained with a U(1) gauge-theory, where the gap in the spin-wave spectrum determines the strength of the gauge-fields. They mediate an attractive long-range interaction whose possible bound-states correspond to charge-spin separation and pairing.Comment: 11 pages, LaTex, chris-preprint-1994-