Gauge fixing, zero--momentum modes and the calculation of masses on a lattice

It is shown that the zero--momentum modes can strongly affect the values of the masses, for example the magnetic screening mass $m_m$, calculated from gauge--dependent correlators with zero momentum.Comment: 8 pages, uuencoded Latex file and one figure (eps-file

The photon propagator in compact QED_{2+1}: the effect of wrapping Dirac strings

We discuss the influence of closed Dirac strings on the photon propagator in the Landau gauge emerging from a study of the compact U(1) gauge model in 2+1 dimensions. This gauge also minimizes the total length of the Dirac strings. Closed Dirac strings are stable against local gauge-fixing algorithms only due to the torus boundary conditions of the lattice. We demonstrate that these left-over Dirac strings are responsible for the previously observed unphysical behavior of the propagator of space-like photons (D_T) in the deconfinement (high temperature) phase. We show how one can monitor the number N_3 of thermal Dirac strings which allows to separate the propagator measurements into N_3 sectors. The propagator in N_3 \neq 0 sectors is characterized by a non--zero mass and an anomalous dimension similarly to the confinement phase. Both mass squared and anomalous dimension are found to be proportional to N_3. Consequently, in the N_3=0 sector the unphysical behavior of the D_T photon propagator is cured and the deviation from the free massless propagator disappears.Comment: 13 pages, 13 figures, 1 tabl

Intertwining Operator Realization of the AdS/CFT Correspondence

We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of representation equivalence between representations of the conformal group describing the bulk AdS fields $\phi$ and the coupled boundary fields $\phi_0$ and ${\cal O}$. We use two kinds of equivalences. The first kind is equivalence between bulk fields and boundary fields and is established here. The second kind is the equivalence between coupled boundary fields. Operators realizing the first kind of equivalence for special cases were given by Witten and others - here they are constructed in a more general setting from the requirement that they are intertwining operators. The intertwining operators realizing the second kind of equivalence are provided by the standard conformal two-point functions. Using both equivalences we find that the bulk field has in fact two boundary fields, namely, the coupled boundary fields. Thus, from the viewpoint of the bulk-boundary correspondence the coupled fields are on an equal footing. Our setting is more general since our bulk fields are described by representations of the Euclidean conformal group $G=SO(d+1,1)$, induced from representations $\tau$ of the maximal compact subgroup $SO(d+1)$ of $G$. From these large reducible representations we can single out representations which are equivalent to conformal boundary representations labelled by the conformal weight and by arbitrary representations $\mu$ of the Euclidean Lorentz group $M=SO(d)$, such that $\mu$ is contained in the restriction of $\tau$ to $M$. Thus, our boundary-to-bulk operators can be compared with those in the literature only when for a fixed $\mu$ we consider a 'minimal' representation $\tau=\tau(\mu)$ containing $\mu$.Comment: 25 pages, TEX file using harvmac.tex; v2: misprints corrected; to appear in Nuclear Physics

Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

Mass gap and finite-size effects in finite temperature SU (2) lattice gauge theory

Engels J, Mitrjushkin VK. Mass gap and finite-size effects in finite temperature SU (2) lattice gauge theory. Physics Letters, B. 1992;282(3-4):415-422.This letter is devoted to the investigation of the point-point Polyakov loop correlators in SU (2) lattice gauge theory on 4Ns3 lattices with Ns=8, 12, 18 and 26. We use an analytic expression for point-point correlators provided by the transfer matrix formalism to study the temperature dependence of the mass gap [mu]m.g. and the corresponding matrix element [nu] near the critical point in a finite volume. The finite-size scaling analysis of the values [mu]m.g.([beta];Ns) obtained gives the possibility to extract the critical value [beta]c, the critical exponent [nu] and the surface tension [alpha]s.t