Volume independence in large Nc QCD-like gauge theories

Volume independence in large \Nc gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large \Nc orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large \Nc ``orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large \Nc equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large \Nc QCD in infinite volume.Comment: 32 pages, 4 figure

Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories

Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.Comment: 21 page, JHEP styl

Universal properties of thermal and electrical conductivity of gauge theory plasmas from holography

We propose that for conformal field theories admitting gravity duals, the thermal conductivity is fixed by the central charges in a universal manner. Though we do not have a proof as yet, we have checked our proposal against several examples. This proposal, if correct, allows us to express electrical conductivity in terms of thermodynamical quantities even in the presence of chemical potential.Comment: 13 pages, appendix added, close to journal versio

A transport coefficient: the electrical conductivity

I describe the lattice determination of the electrical conductivity of the quark gluon plasma. Since this is the first extraction of a transport coefficient with a degree of control over errors, I next use this to make estimates of other transport related quantities using simple kinetic theory formulae. The resulting estimates are applied to fluctuations, ultra-soft photon spectra and the viscosity. Dimming of ultra-soft photons is exponential in the mean free path, and hence is a very sensitive probe of transport.Comment: Talk given in ICPAQGP 2005, SINP, Kolkat

First search for double-beta decay of 184Os and 192Os

A search for double-beta decay of osmium has been realized for the first time with the help of an ultra-low background HPGe gamma detector at the underground Gran Sasso National Laboratories of the INFN (Italy). After 2741 h of data taking with a 173 g ultra-pure osmium sample limits on double-beta processes in 184Os have been established at the level of T_{1/2} about 10^{14}-10^{17} yr. Possible resonant double-electron captures in 184Os were searched for with a sensitivity T_{1/2} about 10^{16} yr. A half-life limit T_{1/2} > 5.3 10^{19} yr was set for the double-beta decay of 192Os to the first excited level of 192Pt. The radiopurity of the osmium sample has been investigated and radionuclides 137Cs, 185Os and 207Bi were detected in the sample, while activities of 40K, 60Co, 226Ra and 232Th were limited at the mBq/kg level.Comment: 12 pages, 7 figures, 2 table

Search for 2\beta\ decays of 96Ru and 104Ru by ultra-low background HPGe gamma spectrometry at LNGS: final results

An experiment to search for double beta decay processes in 96Ru and 104Ru, which are accompanied by gamma rays, has been realized in the underground Gran Sasso National Laboratories of the I.N.F.N. (Italy). Ruthenium samples with masses of about (0.5-0.7) kg were measured with the help of ultra-low background high purity Ge gamma ray spectrometry. After 2162 h of data taking the samples were deeply purified to reduce the internal contamination of 40K. The last part of the data has been accumulated over 5479 h. New improved half life limits on 2\beta+/\epsilon \beta+/2\epsilon\ processes in 96Ru have been established on the level of 10^{20} yr, in particular for decays to the ground state of 96Mo: T1/2(2\nu 2\beta+) > 1.4 10^{20} yr, T1/2(2\nu \epsilon\beta+) > 8.0 10^{19} yr and T1/2(0\nu 2K) > 1.0 10^{21} yr (all limits are at 90% C.L.). The resonant neutrinoless double electron captures to the 2700.2 keV and 2712.7 keV excited states of 96Mo are restricted as: T1/2(0\nu KL) > 2.0 10^{20} yr and T1/2(0\nu 2L) > 3.6 10^{20} yr, respectively. Various two neutrino and neutrinoless 2\beta\ half lives of 96Ru have been estimated in the framework of the QRPA approach. In addition, the T1/2 limit for 0\nu 2\beta- transitions of 104Ru to the first excited state of 104Pd has been set as > 6.5 10^{20} yr.Comment: 14 pages, 5 figures, 2 tables; version accepted for publication on Phys. Rev.

Center symmetry and the orientifold planar equivalence

We study the center symmetry of SU(N) gauge theories with fermions in the two-index representations, by computing the effective potential of the Polyakov loop in the large-mass expansion on the lattice. In the large-N limit and at non-zero temperature, we find that the center symmetry is Z_N for fermions in the adjoint representation and just Z_2 for fermions in the (anti)symmetric representation. We discuss the fact that our results do not contradict the orientifold planar equivalence, which relates a common sector defined by the bosonic gauge-invariant C-even states of theories with fermions in different two-index representations. Our results complement the work of Armoni et al. (2007), who showed how at zero temperature a Z_N center symmetry is dynamically recovered also for fermions in the (anti)symmetric representation, by considering the theories at finite temperature.Comment: 27 pages, 7 eps figure

Large N reduction on group manifolds

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant and SO(4) invariant manner.Comment: 21 pages, 4 figures, typos corrected, a reference adde