Gauge field theory for Poincar\'{e}-Weyl group

On the basis of the general principles of a gauge field theory the gauge theory for the Poincar\'{e}-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions from true gauge fields: Lorentzian, translational and dilatational ones. The equations of gauge fields which sources are an energy-momentum tensor, orbital and spin momemta, and also a dilatational current of an external field are obtained. A new direct interaction of the Lorentzian gauge field with the orbital momentum of an external field appears, which describes some new effects. Geometrical interpretation of the theory is developed and it is shown that as a result of localization of the Poincar\'{e}-Weyl group spacetime becomes a Weyl-Cartan space. Also the geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is proposed.Comment: LaTex, 27 pages, no figure

Stringy effect of the holographic correspondence for Dp-brane backgrounds

Based on the holographic conjecture for superstrings on Dp-brane backgrounds and the dual (p+1)-dimensional gauge theory ($0\le p\le 4$) given in hep-th/0308024 and hep-th/0405203, we continue the study of superstring amplitudes including string higher modes ($n\ne 0$). We give a prediction to the two-point functions of operators with large R-charge J. The effect of stringy modes do not appear as the form of anomalous dimensions except for p=3. Instead, it gives non-trivial correction to the two-point functions for supergravity modes. For p=4, the scalar two-point functions for any n behave like free fields of the effective dimension d_{eff}=6 in the infra-red limit.Comment: 23 pages, typos correcte

Proper Motions and CCD-photometry of Stars in the Region of the Open Cluster Trumpler 2

The results of the complex study of galactic open cluster Trumpler 2 are presented. In order to obtain the proper motions the positions of 2600 stars up to the limit magnitude B ~ 16.25 mag in the area 80x80 arcmin around the cluster were measured on 6 plates with the maximal epoch difference of 63 years. The root-mean error of the relative proper motions is 4.2 mas/yr. The catalogue of BV magnitudes of all the stars in the investigated area was compiled. Astrometric selection of the cluster members within the region of R<16 arcmin from the center of the cluster was made by means of the W.Sanders method. In that field 192 stars were found to have the individual membership probability greater then 85%, 148 of them are situated within the +/-3sigma_(B-V) band around the main sequence of the cluster. They are considered to be cluster members by two criteria. The U-B ~ B-V diagram plotted for the astrometrical cluster members by the data taken from the Washington catalogue of the UBV photometry in the galactic cluster fields (Hoag et al.1961) made it possible to redefine the value of the color excess E(B-V)=0.40 mag. The superposition of the MS of the cluster with the ZAMS Schmidt-Kaler leads to the coincidence at the value of the apparent distance module (V-Mv)=10.50 which corresponds to the distance r=725 pc. The luminosity and mass functions of the Trumpler 2 were constructed and the value of the slope Gamma=-1.90+/-0.22 was determined. The cluster age of 8.913x10^7 yr was determined. It is shown that the red giant on the late stage of the evolution (st N.1095) belongs to cluster and indicates the brightness variability. The possibility that the number of both known and recently discovered variables are cluster members was considered. Tables 2,3,3A,5 will be only available in the electronic form.Comment: 14 pages, 7 figure

Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators

It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6) angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which limit they are effectively tensionless; when J=0, supersymmetry is enhanced to 1/4. These results imply that recent checks of the AdS/CFT correspondence actually test a nearly-BPS sector.Comment: 12 pages, no figures; v2: new section on CFT operators and new references added, discussion section and acknowledgements modified, abstract rephrashe

A note on spin chain/string duality

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.Comment: v.2 One reference added, typos corrected, 21 page

Spiky Strings, Giant Magnons and beta-deformations

We study rigid string solutions rotating on the S^3 subspace of the beta-deformed AdS_5xS^5 background found by Lunin and Maldacena. For particular values of the parameters of the solutions we find the known giant magnon and single spike strings. We present a single spike string solution on the deformed S^3 and find how the deformation affects the dispersion relation. The possible relation of this string solution to spin chains and the connection of the solutions on the undeformed S^3 to the sine-Gordon model are briefly discussed.Comment: 20 pages, 2 figures; v2: typos corrected, references adde

Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators

We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator carrying a certain set of quantum numbers defines a singular solution. We show in a number of examples that this solution coincides with the classical string solution with the same quantum numbers but written in a different two-dimensional coordinate system. The marginality condition imposed on an operator yields a relation between the energy and the other quantum numbers which is shown to coincide with that of the corresponding classical string solution. We also argue that in some cases vertex operators in AdS_5 x S^5 cannot be given by expressions similar to the ones in flat space and a more involved consideration is required.Comment: 23 pages, 1 Figur

Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds

We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex deformation of N=4 SYM, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the coordinate space Bethe ansatz, calculate the S-matrix and determine for which choices of parameters the S-matrix fulfills the Yang-Baxter equations. For these choices of parameters we furthermore write down the R-matrix. We find in total four classes of integrable models. In particular, each already known model of the above type is nothing but one in a family of such models.Comment: 16 pages, 3 figures, references correcte

Precision Spectroscopy of AdS/CFT

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weights of the corresponding non-near-BPS operators in planar N=4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the `t Hooft coupling lambda. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in lambda. This one-loop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly non-trivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.Comment: 26 pages, 1 figure, v2: typos correcte

Formation of the Upstream Region in HV Gas Blast Interrupters with Synchronous Gas Injection

The problem of a synchronous gas injection at the vicinity of current zero for high voltage gas blast circuit breakers~(GCB) is discussed. The basic aim of the investigation is to improve the efficiency of arc quenching in GCB by increasing interruption ability without changes in drive parameters. The paper reviews the upstream region influence on the interruption capability, gas injection - mass flow interactions at the region between electrical contact and nozzle throat of GCB. Numerical simulation is used to calculate gas--dynamics parameters at the upstream region of mono--flow GCB. The mass discharged as a result of the synchronous gas injection can rapidly modify both the density and pressure at the nozzle throat, regulate flow velocity in the research region. The selected method of the gas injection effects the breaking performance in the arc quenching device strongly. Some calculation results are presented.