BPS states in string theory

In this thesis we discuss a number of interesting and important properties of BPS states in string theory. We study wall-crossing behavior of BPS states at large volume limit and implications of it for the OSV conjecture. We find that the weak topological coupling OSV conjecture can be true at most in a special chamber of the K"ahler cone. We also clarify an interesting puzzle arising in the description of BPS states on the Higgs branch of supersymmetic quantum mechanics. Using methods of toric geometry we compute Hilbert spaces of BPS states on the compactified Higgs branch and arrive at completely consistent picture of spatial $Spin(3)$ structure of those spaces. We introduce new kinds of walls, called Bound State Transformation(BST) walls, in the moduli space across which the nature of BPS bound states changes but the index remains continuous. These walls are necessary to explain the continuity of BPS index. BPS states can undergo recombination, conjugation or hybrids of the two when crossing a BST wall. Conjugation phenomenon happens near singularities in the moduli space and we relate massless spectra of BPS states at such singularities to monodromies around them. In cases when massless vector BPS particles are present we find new constraints on the spectrum and in particular predict the existence of magnetic monopoles becoming massless at such singularities. We give a simple physical derivation of the Kontsevich-Soibelman wall-crossing formula. Considering galaxy-like configurations of BPS particles with a central supermassive black hole with a number of stellar BPS systems around it we derive a consistency requirement on the partition function of such BPS galaxies. This requirement turns out to be nothing but Kontsevich-Soibelman wall-crossing formula. Our approach gives a generalization of the formula for the case when massless BPS particles are present.Ph.D.Includes bibliographical referencesIncludes vitaby Evgeny Andriyas