Aspects of String/Gauge Theory Duality

The most fundamental constituents of the matter are the subject of quantum field theories. Their interactions are classified according to their strength and are assumed to be unified at very high energies. The weak interaction strength allows the application of the perturbation theory which predicts with a remarkable accuracy many observable phenomena. The complete understanding of the gauge fields at strong coupling remains one of the most involving challenges and no universal approach is known. The dualities in gauge theories usually relate strong and weak coupling regimes. The idea of deep relation between string theory and gauge fields emerged long time ago. It is based on the description of the flux tubes connecting strongly interacting objects by an effective string theory at distances larger than the thickness of the tubes. This interpretation underwent dramatic metamorphosis ending up with a large class of gauge theories that are exactly equivalent to strings. The contemporary understanding is that strings propagate in higher dimensional space while the gauge theory is defined on its boundary. The gauge theory is considered as a projection of the strings on the boundary but as real flux tubes. The strings on other hand can be reconstructed from gauge theory data and the correspondence is called holographic. Surprising feature of this correspondence is the duality between the two theories. The importance of investigation of string/gauge theory dualities is dictated from the fact that the knowledge of the weak coupling regime of one of the theories can be translated to the strong coupling of the other. The aim of our project is to deepen the understanding and to extend the scope of string theory description of various gauge theories. Its core is composed of objectives on development of string/gauge theory correspondence as well as applications to gauge theory phenomena.

The most fundamental constituents of the matter are the subject of quantum field theories. Their interactions are classified according to their strength and are assumed to be unified at very high energies. The weak interaction strength allows the application of the perturbation theory which predicts with a remarkable accuracy many observable phenomena. The complete understanding of the gauge fields at strong coupling remains one of the most involving challenges and no universal approach is known. The dualities in gauge theories usually relate strong and weak coupling regimes. The idea of deep relation between string theory and gauge fields emerged long time ago. It is based on the description of the flux tubes connecting strongly interacting objects by an effective string theory at distances larger than the thickness of the tubes. This interpretation underwent dramatic metamorphosis ending up with a large class of gauge theories that are exactly equivalent to strings. The contemporary understanding is that strings propagate in higher dimensional space while the gauge theory is defined on its boundary. The gauge theory is considered as a projection of the strings on the boundary but as real flux tubes. The strings on other hand can be reconstructed from gauge theory data and the correspondence is called holographic. Surprising feature of this correspondence is the duality between the two theories. The importance of investigation of string/gauge theory dualities is dictated from the fact that the knowledge of the weak coupling regime of one of the theories can be translated to the strong coupling of the other. The aim of our project is to deepen the understanding and to extend the scope of string theory description of various gauge theories. Its core is composed of objectives on development of string/gauge theory correspondence as well as applications to gauge theory phenomena.