[en] Short communication

[en] We discuss some aspects of stochastic quantization of gauge theories in the spirit of Parisi and Wu. We show that it is not compatible with dimensional regularization umless we suppress the noise associated with ciclic variables. (author)

[en] Published in summary form only

[en] We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing the flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of any additional assumptions such as couplings of the ghost condensate to secondary fields, and suggests that violation of the null energy condition may be the true source of pathology in these theories.

[en] We investigate conformal symmetries of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory for multiple M2 branes and the Lorentzian Bagger-Lambert-Gustavsson (L-BLG) theory which can be obtained by taking a scaling limit k(>>N)→∞ of the ABJM theory. The conformal symmetry is maintained in the L-BLG by considering general space-time varying solutions to the constraint equations. The dual geometry is reduced to d=10AdS₄xCP³ in the scaling limit and has the same conformal symmetry. The curvature radius R satisfies l_p⁽¹¹⁾<< l_p⁽¹⁰⁾<< R<< l_s (l_p^(d) and l_s are the d-dimensional Planck lengths and the string scale), and the theory is in a region where an α^' expansion is not valid. We also study how the SO(8) covariance is recovered in the AdS₄xCP³ geometry by taking the scaling limit.

[en] We propose a new approach towards the understanding of confinement. Starting from an anisotropic five-dimensional pure gauge theory, we approach a second order phase transition where the system reduces dimensionally. Dimensional reduction is realized via localization of the gauge and scalar degrees of freedom on four-dimensional branes. The gauge coupling deriving from the brane Wilson loop observable runs like an asymptotically free coupling at short distance, while it exhibits clear signs of string formation at long distance. The regularization used is the lattice. We take the continuum limit by keeping the ratio of the lattice spacing in the brane over the lattice spacing along the extra dimension constant and smaller than one.

[en] In the context of the 1/N expansion, the validity of the Slavnov-Taylor identity relating three- and two-point functions for the 2+1-dimensional noncommutative CP^N-1 model is investigated, up to subleading 1/N order, in the Landau gauge.

[en] We discuss some renormalization problems that arise at one loop in noncommutative gauge theories in 4D. It is shown that the the noncommutative U(N) theory is one-loop renormalizable. When the analysis is then extended to the noncommutative orthogonal gauge theories we find that for one-loop amplitudes the situation is more problematic

[en] A derivation of the basis of states for the SM(2,4_k) superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension 2κ - 1/2. The basis is expressed solely in terms of G_r modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with (2κ - 1)-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors

[en] Two pillars of an effect of discrete asymmetry are discussed: 1) the breaking the corresponding symmetry at the basic level (that of the Lagrangian maybe); 2) the manifestation of asymmetry at the level of the square of modulus of the amplitude.The classification of possible types of symmetry breaking leads us to 'CPT cube'. The subtleties of asymmetry manifestations are illustrated by simple examples. (author)