Modern Physics Letters A

The spherically symmetric singular perfect fluid shells are considered when their radii are equal to the event horizon (the black shells). We study their observable masses, depending at least on the three parameters, viz. the square speed of sound in the shell, instantaneous radial velocity of the shell at a moment when it reaches the horizon, and integration constant related to surface mass density. We discuss the features of black shells depending on the equation of state.

We calculate the topological self-energy of the stationary linear distribution of a four-current with zero total current and a charge per unit length in the space–time of a straight cosmic string. It is shown that if the structure of a current is determined in the first approximation by its electric and magnetic dipole moments, then the self-force is not equal to zero and the current is also affected by the action of a moment of force which has a topological nature. The generalization of the obtained results for the space–time of multiple cosmic string is also discussed.

We present the Lax operator for the N=3 KdV hierarchy and consider its extensions. We also construct a new infinite family of N=2 supersymmetric hierarchies by exhibiting the corresponding super Lax operators. The new realization of N=4 supersymmetry on the two general N=2 superfields, bosonic spin-1 and fermionic spin-1/2, is discussed.

In the background of a central Coulomb potential, the Schrödinger and Dirac equations lead to exactly solvable spectral problems. When the Schrödinger–Coulomb equation is supplemented by a Harmonic potential, the corresponding spectral problem still possesses a finite number of algebraic solutions: it is quasi-exactly solvable. In this letter we analyze the spectral problem corresponding to the Dirac–Coulomb problem supplemented by a linear radial potential and we show that it also leads to quasi-exactly solvable equations.

We consider generic MQCD configurations with matter described by semi-infinite D4-branes and softly broken supersymmetry. We show that the matter sector does not introduce supersymmetry breaking parameters so that the most relevant supersymmetry breaking operator at low energies is the gaugino mass term. By studying the run-away properties of these models in the decoupling limit of the adjoint matter, we argue that these softly broken MQCD configurations fail to capture the infrared physics of QCD at scales below the gaugino mass.

In the M(atrix) theory by making the expansions of the matrices around the infinite membrane and four-brane solutions, we derive the three- and five-dimensional gauge theories in the dual space–times. The explicit forms of solutions yield the dual coordinates and each expansion is related to a toroidal compactification of the M(atrix) theory. We also analyze the expansion around the finite membrane. From the derived Lorentz and gauge-invariant actions, the gauge coupling constants are shown to be characterized by the volumes of tori.

It is shown that all three-body quantal integrable systems that emerge in the Hamiltonian reduction method possess the same hidden algebraic structure. All of them are given by a second degree polynomial in generators of an infinite-dimensional Lie algebra of differential operators.

In this letter a screening current or contour representation is given for certain quantum superalgebras. The Gomez–Sierra construction of quantum groups in conformal field theory is generalized to cover superalgebras and illustrated using recent results on screening currents in affine current superalgebra.

We describe U(N)-monopoles (N>1) on Kerr black holes using the parameters of the moduli space of holomorphic vector U(N)-bundles over with the help of the Grothendieck splitting theorem. For N = 2,3 we obtain this description in an explicit form as well as the estimates for the corresponding monopole masses. This gives us a possibility to adduce some reasonings in favor of the existence of both a fine structure for Kerr black holes and the statistical ensemble tied with it which might generate the Kerr black hole entropy.