D-branes in Supersymmetric Backgrounds

TL;DR

This thesis explores extending the AdS/CFT correspondence to less supersymmetric theories by analyzing supersymmetric D-brane configurations in type IIB backgrounds dual to N=1 gauge theories, including probe and backreacted solutions.

Contribution

It systematically studies supersymmetric D-branes in N=1 supergravity backgrounds and develops techniques to incorporate backreaction from flavor branes, advancing the understanding of gauge/gravity dualities.

Findings

Identification of supersymmetric D-brane configurations in AdS_5xY^{p,q} and L^{a,b,c} backgrounds.

Checks of the correspondence between D-branes and chiral operators in dual gauge theories.

Development of methods to include backreaction of flavor branes, matching gauge theory features.

Abstract

In this Ph. D. Thesis we concentrate on the study of the extension of the AdS/CFT correspondence to theories with less supersymmetry. In particular, we search for the possibility of adding supersymmetric D-branes in type IIB supergravity solutions which are dual to N=1 supersymmetric gauge theories in four dimensions. In the probe approximation we perform a systematic analysis of the possible supersymmetric D-brane configurations in backgrounds dual to N=1 superconformal field theories, firstly in the AdS_5xY^{p,q} solutions and then in their generalisation to the AdS_5xL^{a,b,c} backgrounds. Some checks of the correspondence between D-brane configurations and chiral operators of the dual gauge theory are performed. We also analyse the possible supersymmetric D5-brane configurations dual to defects (of codimension one and two) in N=1 SYM theory in the framework of the Maldacena-Nunez solution. Beyond the probe approximation, we develop techniques in order to take into account the backreaction undergone by the type IIB supergravity solutions (dual to N=1 superconformal field theories and their extensions to cascading theories) due to the addition of a number of flavour branes of the same order as the number of colour branes which generate the unflavour background. The dual interpretation of those flavour branes is given in terms of dynamical fields transforming in the fundamental representation of the gauge group. Several gauge theories features are matched, like beta functions, anomalies and the duality cascade which describes the RG flow of the cascading field theories.