STUDY ON DUALITY BETWEEN OPEN-AND CLOSED-STRINGS

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(i)We exploit the boundary state formalism to investigate duality between open-and closed-strings in superstring theory. By using the off-shell interactions of open-and closed-strings developed in our for- malism, we show that in the background of non-vanishing NS-NS two-form field, the masssive modes of closed-string emerge as the Wilson lines in non-commutative gauge theories on D-branes. (ii)In superstring compactifications, local Calabi-Yau geometries are related with thermodynamic quantities of certain statistical models. We study random plane partitions relevant to describe Nekrasov's par- tition functions of five-dimensional supersymmetric gauge theories, from both the gauge theory and gravity viewpoints. After taking a natural scaling, the thermodynamic limit corresponds to a classical limit with respect to g_<st>. We show that classical objects called the limit shapes of plane partition govern the systems. In particular, the limit shapes at zero temperature are equivalent to the local geometries while at finite temperature, they describe a quantum deformation of the local geometries.