Hamiltonian lattice gauge models and the Heisenberg double

Hamiltonian lattice gauge models based on the assignment of the Heisenberg double of a Lie group to each link of the lattice are constructed in arbitrary space-time dimensions. It is shown that the corresponding generalization of the gauge-invariant Wilson line observables requires to attach to each vertex of the line a vertex operator which goes to the unity in the continuum limit.Comment: 10 pages, latex, no figure

Gauge-invariant Hamiltonian formulation of lattice Yang-Mills theory and the Heisenberg double

It it known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge $A_{0}=0$ one should place on every link the cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting case of a so called Heisenberg double of a Lie group which is one of the basic objects in the theory of Lie-Poisson and quantum groups. It is shown in the paper that there is a generalization of the usual Hamiltonian formulation to the case of the Heisenberg double.Comment: 11 pages, latex, no figure

Thermonuclear burn-up in deuterated methane CD4CD_4

The thermonuclear burn-up of highly compressed deuterated methane CD$_4$ is considered in the spherical geometry. The minimal required values of the burn-up parameter $x = \rho_0 \cdot r_f$ are determined for various temperatures $T$ and densities $\rho_0$. It is shown that thermonuclear burn-up in $CD_4$ becomes possible in practice if its initial density $\rho_0$ exceeds $\approx 5 \cdot 10^3$ $g \cdot cm^{-3}$. Burn-up in CD$_2$T$_2$ methane requires significantly ($\approx$ 100 times) lower compressions. The developed approach can be used in order to compute the critical burn-up parameters in an arbitrary deuterium containing fuel

Stationary strings near a higher-dimensional rotating black hole

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration which crosses the infinite red-shift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a spacetime with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string.Comment: 13 pages, contains additianal material at the end of Section 8, also small misprints are correcte

Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence

We compute the conformal anomaly of free d=6 superconformal (2,0) tensor multiplet on generic curved background. Up to a trivial covariant total-derivative term, it is given by the sum of the type A part proportional to the 6-d Euler density, and the type B part containing three independent Weyl invariants. Multiplied by factor 4N^3, the type B part of the anomaly reproduces exactly the corresponding part of the conformal anomaly of large N multiple M5-brane (2,0) theory as predicted (hep-th/9806087) by the AdS/CFT correspondence. The coefficients of the type A anomaly differ by the factor 4/7 x 4 N^3, so that the free tensor multiplet anomaly does not vanish on a Ricci-flat background. The coefficient 4N^3 is the same as found (hep-th/9703040) in the comparison of the tensor multiplet theory and the d=11 supergravity results for the absorption cross-sections of gravitons by M5 branes, and in the comparison (hep-th/9911135) of 2- and 3-point stress tensor correlators of the free tensor multiplet with the AdS_7 supergravity predictions. The reason for this coincidence is that the three Weyl-invariant terms in the anomaly are related to the $h^2$ and $h^3$ terms in the near flat space expansion of the corresponding non-local effective action, and thus to the 2-point and 3-point stress tensor correlators in flat background. At the same time, the type A anomaly is related to the $h^4$ term in the non-local part of the effective action, i.e. to a certain structure in the 4-point correlation function of stress tensors.Comment: 20 pages, latex. v2: minor corrections, references adde