Introduction. A classical dynamical r-matrix is an l-equivariant function r : l∗ → g ⊗ g (where l, g are Lie algebras), such that r21 + r = Ω is g-invariant, which satisfies the classical dynamical Yang-Baxter equation (CDYBE). CDYBE is a differential equation, which generalizes the usual classical Yang-Baxter equation. It was introduced in 1994 by G.Felder [Fe], in the context of conformal fie...

The AdS/CFT correspondence, or in a more general sense, the gauge/gravity correspondence, is a duality between a string theory or gravity defined on one space and a gauge theory living on the conformal boundary of the same space. The AdS/CFT correspondence has drawn a tremendous amount of attention since the late 1990’s. After all, it sounds so promising and exciting to connect two drastically ...

We review the existing weak-coupling results on the thermodynamic potential of deconfined QCD at small and large quark chemical potential and compare with results from lattice gauge theory as well as the exactly solvable case of large-N f QCD. We also discuss the new analytical results on non-Fermi-liquid effects in entropy and specific heat as well as in dispersion laws of quark quasiparticles...

We analyze a gauge-Higgs unification model which is based on a gauge theory defined on a six-dimensional spacetime with an S2 extra-space. We impose a symmetry condition for a gauge field and non-trivial boundary conditions of the S2. We provide the scheme for constructing a four-dimensional theory from the six-dimensional gauge theory under these conditions. We then construct a concrete model ...

This thesis carries out a detailed investigation of the action for pure YangMills theory which L. Mason formulated in twistor space. The rich structure of twistor space results in greater gauge freedom compared to the theory in ordinary space-time. One particular gauge choice, the CSW gauge, allows simplifications to be made at both the classical and quantum level. The equations of motion have ...

For the gauge couplings, which arise after toroidal compactification of six–dimensional heterotic N=1 string theories from the T 2 torus, we calculate their one–loop corrections. This is performed by considering string amplitudes involving two gauge fields and moduli fields. We compare our results with the equations following from N=2 special geometry and the underlying prepotential of the theo...

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

Quantum field theories based on noncommutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model, which can uniquely describe the strong and electroweak interactions, has been constructed. This prevents consistent and systematic study of noncommutative space-time. In this work we construct a NCQFT model based on the trinification gauge group SU(3)C × SU(3)L × SU(...

A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator. 1. It is well known that a gauge symmetry leads to constraints on dynamical variables in the theory [1]. Therefore, the evolution of unphysical degrees of freedo...