There are many examples in physics when dynamics of the system in question can be shown to be integrable, i.e. entirely determined by the algebraic structure underlying its symmetries. It seems that the integrability is an emerging new principle of Nature, universal and ubiquitous. In particular, there are many recent examples of appearance of the integrable structure (exactly solvable non-linear partial differential equations) in quantum field theories (Yang-Mills theories), condensed matter systems (quantum Hall systems and various growth phenomena) and string theory models (matrix models, non-critical string theories).
The current project aims at exploration of the integrable structure of these and other phenomena and exploiting the powerful mathematical apparatus of the theory of integrable systems for gaining new information and proving new results in the fields of both condensed matter and particle physics. In particular, it is suggested to apply these methods to analytically construct conformal field theory description of edge-excitations of quantum Hall systems (both integer and fractional cases) as well as to the description of fingering in growth phenomena (such as e.g. Laplacian growth). Both are long-standing problems with wide range of both theoretical and experimental consequences. It is also proposed to use literally the same methods to describe quite different physically, but surprisingly close mathematically phenomena in the description of low-energy effective theories of (super-symmetric) gauge theories and their description in the language of string theory, as well as to different models of quantum gravity.
The progress here will come from the fact that integrable system has an exact non-perturbative description, thus overcoming the main difficulty of the strongly correlated systems (of which both non-Abelian gauge theories and gravity are examples) - limited applicability of the perturbative description.
Call for proposal
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