Large-N Universality of the Two-Dimensional Yang-Mills String

We exhibit the gauge-group independence (``universality'') of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the string theory reformulation of these gauge theories. By constructing an isomorphism between the string maps contributing to normalized Wilson loop expectation values in the different theories, we prove the large N universality of these observables on any surface. The string calculation of the Wilson loop expectation value on the sphere also leads to an indication of the large N phase transition separating strong- and weak-coupling phases.Comment: 18 pages, phyzzx macro, no figure

Topology on the lattice; 2d Yang-Mills theories with a theta term

We study two-dimensional U($N$) and SU($N$) gauge theories with a topological term on arbitrary surfaces. Starting from a lattice formulation we derive the continuum limit of the action which turns out to be a generalisation of the heat kernel in the presence of a topological term. In the continuum limit we can reconstruct the topological information encoded in the theta term. In the topologically trivial cases the theta term gives only a trivial shift to the ground state energy but in the topologically nontrivial ones it remains to be coupled to the dynamics in the continuum. In particular for the U($N$) gauge group on orientable surfaces it gives rise to a phase transition at $\theta= \pi$, similar to the ones observed in other models. Using the equivalence of 2d QCD and a 1d fermion gas on a circle we rewrite our result in the fermionic language and show that the theta term can be also interpreted as an external magnetic field imposed on the fermions.Comment: 19 pages LaTe

Effect of copper content, initial structure, and scheme of treatment on magnetic properties of ultra-thin grain oriented electrical steel

The effect of the copper content, initial structure, and scheme of treatment on the magnetic properties of an ultra-thin grain oriented electrical steel has been investigated. In the material with copper and an initial sharp texture, the nucleation of new grains upon primary recrystallization is connected with deformation twins; in the samples without copper and with copper and diffuse texture, it is connected predominantly with shear bands and transition bands. Upon heating at a rate of ∼0.004 K/s, the temperature of primary recrystallization in the copper-bearing samples is considerably higher than in the copper-free material. Upon heating at a rate of ∼4 K/s the appearance of new grains occurs almost simultaneously for all of the studied samples. In the samples with copper and initial sharp texture after annealing at 1050 C, a significant part of the volume is occupied by grains that had undergone normal grain growth; in the samples without copper and with copper and diffuse texture, anomalous growth is hardly observed at all. To obtain high final magnetic properties of the ultra-thin grain oriented electrical steel produced by the Littmann method, it has been suggested to use an grain oriented electrical steel with 0.5% Cu that exhibits the diffuse orientation of grains as the workpiece. © 2013 Pleiades Publishing, Ltd

Towards a solution of pure Yang-Mills theory in 3+1 dimensions

We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schr\"odinger representation and the large $N$, planar limit. In particular, within this approach we point out unexpected parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most important parallel shows up in the analysis of the ground state wave-functional especially in view of the numerical similarity of the existing large N lattice simulations of the spectra of 2+1 and 3+1 Yang Mills theories.Comment: 12 page

Pressure-temperature phase diagrams of selenium and sulfur in terms of Patashinski model

The pressure - temperature phase diagrams of Se and S are calculated. Both melting and polymorphous phase transition are described in the frames of statistical Patashinski model. The results are in good agreement with experimental data of Brazhkin et. al.Comment: 3 eps figures, will appear in Physica A, mail to first author [email protected]

The String Calculation of QCD Wilson Loops on Arbitrary Surfaces

Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the 1/N expansion of the Wilson loop expectation values are included.Comment: 10 pages, LaTeX, no figure

A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

Secondary recrystallization in Fe-3% Si alloy with (110)[001] single-component texture

After the primary recrystallization of a preliminarily deformed (110)[001] single crystal, the texture also has the preferred (110)[001] orientation. Furthermore, the texture contains weak orientations, a major part of which is formed at the sample surface and can be described by a spectrum of scattered orientations 120вЊ©210вЊ.351 вЊ©103вЊ. A further heating leads to two concurrent processes taking place in the samples, i.e., the normal growth of Goss grains and secondary recrystallization. Abnormally grown crystals are represented by a quartet of orientations related with the initial Goss orientation by a rotation around [011], [011̄], [101], and [101̄] axes at an angle of ∼30. The crystallographic relationship between the initial and final grain orientations can be explained by their closeness to special misorientations as follows: Σ9, Σ19a, Σ27a, and Σ33a (rotation around 〈110⌠axes to close angles). © 2013 Pleiades Publishing, Ltd

Formation of special misorientations related to transition bands in structure of deformed and annealed single crystal (110)[001] of Fe-3% Si alloy

A transition band between two deformation bands retains for the most part the orientation (110)[001] and shrinks to a thin interlayer or boundary with increasing degree of deformation. At a certain stage of deformation, the microvolumes that are arranged along the interface of the bands become adjusted to special misorientations. During primary recrystallization, cube-on-edge (Goss) grains, which grow from the transition band, have portions of special boundaries common with the deformed matrix; these boundaries were found earlier between the deformation bands. This indicates that the local domains with special misorientations formed at the stage of cold deformation transform during annealing into the corresponding primary-recrystallization nuclei. © 2013 Pleiades Publishing, Ltd

Observation of time quasicrystal and its transition to superfluid time crystal

We report experimental realization of a quantum time quasicrystal, and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid $^3$He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically-long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time super-crystal