Aspects of the Duality between Supersymmetric Yang-Mills Theory and String Theory

University dissertation from Department of Theoretical Physics, Lund University, Sölvegatan 14A S-223 62 Lund, Sweden

Abstract: This thesis deals with three topics related to the Ads/CFT correspondence. In Paper I, solutions describing the geometry of fractional D1-branes of Type IIB string theory are presented. The running coupling constant is computed on the gauge theory side. Paper II uses the idea that the anomalous dimension of a gauge theory operator can be interpreted as an eigenvalue of a spin chain Hamiltonian. The general Leigh-Strassler deformation is rewritten in terms of a spin-one spin chain and the integrability properties of the corresponding Hamiltonian are studied. In paper III a non-commutative multiplication law, a star product, is defined. From this star product the general Leigh-Strassler deformation is obtained, and it is shown that the deformation only results in prefactors to the amplitudes of the undeformed theory.

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