We consider gluon and gluino scattering amplitudes in large N β-deformed N = 4 SYM with real β. A direct inspection of the planar diagrams shows that the scattering amplitudes to all orders in perturbation theory are the same as in the undeformed N = 4 SYM theory. Using the dual σ-model description, we find the same equality at strong coupling to all orders in the σ-model loop expansion. Finall...

We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers: ag := the least cardinal number of maximal cofinitary permutation groups; ap := the least cardinal number of maximal almost disjoint permutation families; c(Sym(N)) := the cofinality of the permutation group on the set of natural numbers. We...

Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly–coupled N =4 SYM plasma at finite temperature. We show that the stochasticity arises at the string world–sheet horizon, and thus is causally disconnected from the black hole horizon in the space–time metric. This hint...

Abstract Let G be a permutation group, acting on set $$\varOmega $$ ? of size n . A subset $${\mathcal {B}}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">B is base for if the pointwise stabilizer $$G_{({\mathcal {B}})}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML"><mm...

We compute certain two-point functions in D = 4, N = 4, SU(N) SYM theory on the Coulomb branch using SUGRA/SYM duality and find an infinite set of first order poles at masses of order (Higgs scale)/(gY M √ N). 1 E-mail: [email protected] 2 E-mail: [email protected] 1. Apart from being a universal way of looking at the gravity/gauge theory relation, Maldacena’s supe...

We investigate the issues of holography and string interactions in the duality between SYM and the pp wave background. We argue that the Penrose diagram of the maximally supersymmetric pp-wave has a one dimensional boundary. This fact suggests that the holographic dual of the pp-wave can be described by a quantum mechanical system. We believe this quantum mechanical system should be formulated ...

The Maldacena-Nuñez solution is generalized to include a number of integration constants, one of which controls the resolution of the singularity of the wrapped D5-brane background. Some features of the dual pure N = 1 super Yang-Mills (SYM) theory are calculated, amongst which the gluino condensate, the beta function of the gauge coupling and a brane probe potential, which is related to the Ve...

Suppose M is an n-dimensional Kähler manifold and L is an ample line bundle over M . Let the Kähler form of M be ωg and the Hermitian metric of L be H. We assume that ωg is the curvature of H, that is, ωg = Ric(H). The Kähler metric of ωg is called a polarized Kähler metric on M . Using H and ωg, for any positive integer m, H 0(M,Lm) becomes a Hermitian inner product space. We use the following...

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...

In this paper we compare the prediction for the high energy soft interaction in N-4 SYM with the experimental data. It is shown that at least half of the total cross section at the LHC energy should have a different source than N=4 SYM.