We review a recent progress in constructing low-energy effective action in N =4 super Yang-Mills theories. Using harmonic superspace approach we consider N =4 SYM in terms of unconstrained N =2 superfield and apply N =2 background field method to finding effective action for N =4 SU(N) SYM broken down to U(1) N−1. General structure of leading low-energy corrections to effective action is discus...

We consider the radial quantization of N = 4 super Yang-Mills (SYM) in 4 dimensions, i.e., N = 4 SYM on a cylinder R × S 3. We construct the generators of superconformal symmetry in the case of U (N) gauge group, generalizing the earlier work by Nicolai et al. for U (1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.

As a motivation, we first recall the possible connection of electric-magnetic duality to finiteness in N = 1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishing of the β-functions at all orders) in N = 1 SYM. Finally, we apply this finiteness criterion to an SU(5) SGUT. The latter turns out to be all-order finite if one imposes additional sy...

The class of finitely presented algebras over a field K with a set of generators a1, . . . , an and defined by homogeneous relations of the form a1a2 · · · an = aσ(a)aσ(2) · · · aσ(n), where σ runs through a subset H of the symmetric group Sym n of degree n, is introduced. The emphasis is on the case of a cyclic subgroup H of Sym n of order n. A normal form of elements of the algebra is obtaine...

Tree amplitudes of 10D supersymmetric Yang-Mills theory (SYM) and 11D supergravity (SUGRA) are collected in multi-particle counterparts of analytic on-shell superfields which have essentially the same form as their chiral 4D counterparts describing N = 4 SYM and N = 8 SUGRA, but with components dependent on a different set of bosonic variables. These are the D=10 and D=11 spinor helicity variab...

denote the algebraic varieties of n n invertible symmetric and skew-symmetric matrices over a eld F, respectively. We rst show how the homotopy type of Sym(n; R) and the homology groups of Sk(n; R) can be determined using an alternative method to Iwasawa decomposition. Then, using recent results of Dimca and Lehrer, the weight polynomials of Sym(n; C) and Sk(n; C) are calculated.

Background: The equation of state (EOS) $E(\ensuremath{\rho},\ensuremath{\delta})$ neutron-rich nucleonic matter at density $\ensuremath{\rho}$ and isospin asymmetry $\ensuremath{\delta}$ can be approximated as the sum symmetric nuclear (SNM) EOS ${E}_{0}(\ensuremath{\rho})$ a power series in ${\ensuremath{\delta}}^{2}$ with coefficient ${E}_{\text{sym}}(\ensuremath{\rho})$ its first term so-ca...

other Rhizobium species. Most of these plasmids encoding for fixation and nodulation properties are non-self transmissible. Plasmid profiles were determined for 24 strains of R. trifolii. All the strains harboured at least three plasmids and as many as eight were present in some strains. Southern hybridization with cloned R. meliloti nifgenes was used to identify indigenous Nif plasmids. Each s...

The availability of fully sequenced bacterial genomes has revealed that many species known to synthesize the polyamine spermidine lack the spermidine biosynthetic enzymes S-adenosylmethionine decarboxylase and spermidine synthase. We found that such species possess orthologues of the sym-norspermidine biosynthetic enzymes carboxynorspermidine dehydrogenase and carboxynorspermidine decarboxylase...

For a graph G = (V,E), a subset F ⊂ V (G) is called an Rk-vertex-cut of G if G − F is disconnected and each vertex u ∈ V (G) − F has at least k neighbors in G − F . The Rk-vertex-connectivity of G, denoted by κ (G), is the cardinality of the minimum Rk-vertex-cut of G, which is a refined measure for the fault tolerance of network G. In this paper, we study κ2 for Cayley graphs generated by k-tr...