The thesis of Peter Svrcek, entitled Studies in Field Theories: MHV Vertices, Twistor Space, Recursion Relations, and Chiral Rings, has been placed on deposit.

Any member of the University wishing to read the thesis may do so. Any objections should be submitted to me in writing. The principal advisor for this work was Professor Ed Witten.

ABSTRACT

In this thesis we study different aspects of four dimensional field theories. In the first chapter we give introduction and overview of the thesis. In the second chapter we review the connection between perturbative Yang-Mills and twistor string theory. Inspired by this, we propose a new way of constructing Yang-Mills scattering amplitudes from Feynman graphs in which the vertices are off-shell continuations of the tree level MHV amplitudes. The MHV diagrams lead to simple formulas for tree-level amplitudes. We then give a heuristic derivation of the diagrams from twistor string theory.

In the third chapter, we explore the twistor structure of scattering amplitudes in theories for which a twistor string theory analogous to the one for N=4 gauge theory has not yet been proposed. We study the differential equations of one-loop amplitudes of gluons in gauge theories with reduced supersymmetry and of tree level and one-loop amplitudes of gravitons in general relativity and supergravity. We find that the scattering amplitudes localize in twistor space on algebraic curves that are surprisingly similar to the N=4 Yang-Mills case.

In the next chapter we propose tree-level recursion relations for scattering amplitudes of gravitons. We use the relations to derive simple formulas for all amplitudes up to six gravitons. We prove the relations for MHV and next-to-MHV amplitudes and the eight graviton amplitudes.

In the last two chapters, we concentrate on the nonperturbative aspects of N=1 gauge theories. Firstly, we find the complete set of relations of the chiral operators of supersymmetric U(N) gauge theory with adjoint scalar. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. We discuss the gaugino condensation in the vacua. Finally, we go on to study the nonperturbative corrections to the Konishi anomaly relations. We show that the Wess-Zumino consistency conditions of the chiral rotations of the matter field imply the absence of the corrections for a wide class of superpotentials.

Daniel Marlow
Chair, Dept. of Physics