[en] We find solutions of 11-dimensional supergravity for M5-branes wrapped on Riemann surfaces. These solutions preserve N = 2 four-dimensional supersymmetry. They are dual to N = 2 gauge theories, including non-conformal field theories. We work out the case of N = 2 Yang-Mills in detail. (author)

[en] We argue that the algebra W_q(n), generated by n pairs of deformed q-bosons, does not allow a Hopf algebra structure. To this end we show that it is impossible to define a comultiplication even for the usual, nondeformed case. We indicate how the comultiplication on U_q[osp(1/2n)] can be used in order to construct representations of deformed (not necessarily Hopf) algebra in tensor products of Fock spaces. (author). 14 refs

[en] The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Nth root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail

[en] By analyzing the conditions for the existence on a space-time L of a global algebraic spinor field [defined as an ideal section of the real spinor Clifford bundle Cl_Spin+(1,3)(L = P_Spin+(1,3)(L x lR_1,3] that represents the (undotted) two component c-spinor field (Weyl spinor field) [defined as a section of a particular real spinor bundle bar S(L) = P_Spin+(1,3) x ρC²] the authors prove the following result known as Geroch's Theorem. A necessary and sufficient condition for L to admit a spinor structure is that the orthonormal frame bundle F₀L have a global section. The authors' proof, that does not use in any stage the complexification of R_1,3 (the space-time Clifford algebra) is very simple, requiring only the explicit construction of the algebraic spinor and the spinoral metric within R_1,3 and elementary facts about associated bundles and the bundle reduction process. This is compared with the original Geroch's proof which uses the full algebraic topology machinery

[en] Perturbative approach to two-dimensional gravity and supergravity is considered. One-loop renormalization of the central charge of SL(2,R) Kac-Moody algebra is calculated perturbatively by functional integration and by explicit calculations of the Feynman diagrams. Also the wavefunction renormalization and the anomalous dimensions in the presence of gravity are calculated

[en] Petrov approach is extended to include a 5-dimensional case according to an algebraic classification of a 4-dimensional space-time without gravitation field for the case of cylindricity by the fifth coordinated. An algebraic classification of a stationary electromagnetic field without sources is performed. This field is considered as a part of the Kaluza space geometry. Examples of such classification are presented

[en] Quasiperiodic systems like Fibonacci strings can be interpreted as orbits of automorphisms of the free group [4]. On the other hand quasiperiodic planar patterns with fivefold symmetry like the Penrose or Triangular Pattern can be derived from the root lattice A₄ [5]. Also the root lattice D₆ is related directly to the icosahedral quasilattice [6]. Motivated by these facts noncommutative models for root lattices based in the automorphisms of the free group or quotients with respect to certain abelian free subgroups are studied. (Author) 6 refs

[en] We review the theoretical basis and the possible applications of Symanzik's improvement program. We discuss also how the program may be extended in such a way to become compatible with the Osterwalder-Schrader positivity. (orig.)

[en] We present results for the 0/sup ++/ glueball mass (m/sub G/) and the string tension (σ) in pure gauge lattice QCD with a four-parameter improved action. We suggest and confirm that previous estimates for m/sub G// √σ have been too low because of the influence of the unphysical and nonuniversal phase structure in the fundamental-adjoint coupling plane. We find that m/sub G/roughly-equal1200-1400 MeV using √σ -- 420 MeV

[en] The thermodynamics of a free massless Bose field is studied on a lattice. The coefficients characterizing finite-size effects are calculated. The use of these corrections in the thermodynamics of Yang-Mills fields makes the Monte Carlo calculations on lattices of different sizes agree with each other