[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] 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] 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 main purpose of the present paper is to study the algebraic and differential geometric properties of n-dimensional g-UFT in Xsub(n). (KAERI)

[en] We propose an algebraic description of (untwisted) D-branes on compact group manifolds G using quantum algebras related to U_q(g). It reproduces the known characteristics of stable branes in the WZW models, in particular their configurations in G, energies as well as the set of harmonics. Both generic and degenerate branes are covered

[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] 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] In this paper we illustrate how the notion of isotopy can be used to solve various problems concerning finite-dimensional division algebras over the real numbers. In particular, we show that the 8-dimensional division algebras which have the same derivation algebra as the octonions, and hence which most resemble the octonions, are not in general isotopes of the octonions. Secondly, using a result of Hopf, we argue that every commutative division algebra is the reals or is isomorphic to a special kind of isotope of the complex numbers. Finally, by considering a certain class of algebras, we show how isotopy is a useful tool for determining necessary and sufficient conditions on the multiplication constants in order to have a division algebra

[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