the degree of φ : S → SU(N), where S is the 3sphere “at infinity” in R. The topological charge has a fermionic description: by the Index Theorem, Q = index(%∂ ) where %∂ A is the Dirac operator coupled to A. The situation is similar for gauge fields on compact manifolds such as S, T , . . . Consider now a family A of SU(N) gauge fields on the 4-torus T 4 parameterized by y ∈ Y (a smooth paramet...

We relate the moduli space of Yang-Mills instantons to quaternionic manifolds. For instanton number one, the Wolf spaces play an important role. We apply these ideas to instanton calculations in N = 4 SYM theory. Instantons in Yang-Mills theories are defined by the solutions to the self-duality equation in four-dimensional Euclidean space, Fμν = Fμν = 1 2ǫμνρσFρσ , (1) and are characterized by ...

We present preliminary results on the proton spin structure function at zero momentum, in the quenched approximation. Our calculation makes use of a nonper-turbative means of determining the multiplicative renormalization of the topological charge density.

Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection between these results and the recent discovery of coherent 3D sheets of topological charge in 4D QCD. In both cases, coherent regions of topological charge form a...

The degenerate crossing number cr∗(G) of a graph G is the minimum number of crossing points of edges in any drawing of G as a simple topological graph in the plane. This notion was introduced by Pach and Tóth who showed that for a graph G with n vertices and e ≥ 4n edges cr∗(G) = Ω(e/n). In this paper we completely resolve the main open question about degenerate crossing numbers and show that c...

In this work we investigate a braneworld scenario where a Kalb-Ramond field propagates, together with gravity, in a five dimensional AdS slice. The rank-2 Kalb-Ramond field is associated with torsion. We study the compactification of the Kalb-Ramond field to four dimensional space-time without gauge fixing, focusing on the effects of torsion. On the brane the Kalb-Ramond field interacts with Aμ...

We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge – the field theoretic and the index definition – is directl...

The effect of repeatedly smearing SU(3) gauge configurations is investigated. Six gauge actions (Wilson, Symanzik, Iwasaki, DBW2, Beinlich-Karsch-Laermann, Langfeld) and three smearing recipes (APE, HYP, EXP, the first two with and without projection) are compared. The impact on Wilson loops and the Creutz ratio is monitored as well as the “naive” topological charge. In the latter case improved...

Using smearing of equilibrium lattice fields generated at finite temperature in the confined phase of SU(2) lattice gauge theory, we have investigated the emerging topological objects (clusters of topological charge). Analysing their monopole content according to the Polyakov gauge and the maximally Abelian gauge, we characterize part of them to correspond to nonstatic calorons or static dyons ...

abstract We find a class of extremal black hole-like global p-brane in higher-dimensional gravity with a negative cosmological constant. The region inside the p-brane horizon possesses all essential features required for the Randall-Sundrum-type brane world scenario. The setup allows to interpret the horizon size as the compactification size in that the Planck scale M Pl is determined by the fu...