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HIGH ENERGY PHYSICS IN THE CONTEXT OF D-BRANE THEORY AND SEARCHES FOR NEW PHYSICS AT THE LHC

In the last decades, we have witnessed the development of soliton theory. This theory had a significant impact on both physics and mathematics. It provided rich material for models of classical field theory. Among these models there are well-known and important applications of equation such as the Korteweg-de Vries equation, the sine-Gordon equation, and others have proven to be well known. The soliton theory is the fusion of the classical theory of linear differential operators, the theory of Lie algebras, elements of geometry, algebra and the theory of derived categories. The theory of derived categories was the starting point for the development of F-theory, superstring theory, and D-brane theory, a modern version of The Theory of Everything. The paper is devoted to the theoretical researches for high-energy soliton objects of type of D-branes. D-brane theory is characterized by a very rich mathematical apparatus, the components of which are category theory, K-theory and homological algebra, which give information about the spectra, masses, decays of D-branes. For the further studying of D-branes their energetic spectra and phase transitions between different soliton states are calculated. By means of package INSTANTON BPS, states are calculated. For investigation of space of modules of Calabi-Yau manifold – the base of D-brane fiber bundle and for calculation the number of generations of quarks and leptons, the Nakamura’s algorithm is applied for calculation the Hilbert scheme for orbifold model. By means of Clifford’s algebra, the topological invariant of D-branes – K-functor is calculated, and the decay of D3-brane into