String theory, dual theories and D-branes

In the context of the Anti-de Sitter / Conformal Field Theory correspondence we consider the Berenstein-Maldacena-Nastase (BMN) sector of the large-N Super Yang-Mills theory and demonstrate explicitly the correspondence of four-impurity operators therein to known states in string theory on the pp-wave background obtained as a Penrose limit of Ads space. In the corresponding gauge theory we calculate matrix elements of the dilatation operator in the BMN operator basis. These matrix elements are found to coincide with those of the light-cone string Hamiltonian, which is computed using the string field theory vertex in the pp-wave background. Our results are in agreement with others' results obtained using gauge-theory three-point functions. We next solve perturbative superstring theory on the Nappi-Witten background, obtaining the bosonic and fermionic spectra, and find that supersymmetry can be preserved in the Penrose limit. Our results indicate that the high-energy sector of little string theory, being holographically dual to the string theory which we solve, retains a supersymmetric spectrum. We perform a semiclassical analysis of strings in the Nappi- Witten metric and find that the relationship between energy and momentum coincides with the known result for a flat background. In the context of Vacuum String Field Theory (VSFT), we put forth some ideas as to how a distinction might be made between 'background7 D-branes, which are encoded explicitly in the formulation of split-string field theory, and 'string-field' D-branes, which correspond to solitonic lump solutions. We use the geometrical surface-state formulation of VSFT to investigate tachyon fluctuations about certain lump solutions, called sliver states, and thereby calculate their tensions. We perform this analysis both with and without a background B-field, and are able to reproduce the standard string-theory results for the ratios of D-brane tensions. We investigate tachyon fluctuations about another state known as the butterfly. As would be expected for a D-brane, the equation of motion derived for the tachyon field corresponds to the requirement that the quadratic term in the string-field action vanish on-shell. We begin a calculation of the tension of the butterfly and conjecture that this too will coincide with the standard D-brane expression.