The Geometry of Fractional D1-branes

We find explicit solutions of Type IIB string theory on R^4/Z_2 corresponding to the classical geometry of fractional D1-branes. From the supergravity solution obtained, we capture perturbative information about the running of the coupling constant and the metric on the moduli space of N=4, D=2 Super Yang Mills.Comment: 13 pages, no figures, minor corrections, clarifications to the text in section

Star product and the general Leigh-Strassler deformation

We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of N=4 SYM. The essential difference from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with charges in a corresponding diagonal matrix, we consider two Z_3-symmetries followed by an SU(3) transformation, with resulting off-diagonal elements. From this procedure we obtain a more general Leigh-Strassler deformation, including cubic terms with the same index, for specific values of the coupling constants. We argue that the conformal property of N=4 SYM is preserved, in both beta- (one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the deformation for each amplitude can be extracted in a prefactor. We also conclude that the obtained amplitudes should follow the iterative structure of MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A added, v4: clarification in section 3.

The general Leigh-Strassler deformation and integrability

The success of the identification of the planar dilatation operator of N=4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.Comment: 22 pages, 8 figures, reference adde

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

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