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.
We consider both the supersymmetric open 2-brane and bosonic open 2-brane, their quantization and spectrum under the flat metric condition. The supersymmetric spectrum turns out to be discrete, while the spectrum of purely bosonic open 2-brane is shown to be devoid of any massless states.
We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for obtaining the correct result.
We derive level-rank duality in pure Chern-Simons gauge theories from a non-supersymmetric Seiberg duality by using a non-supersymmetric brane configuration in type IIB string theory. The brane configuration consists of fivebranes, N D3 antibranes and an O3 plane. By swapping the fivebranes we derive a 3d non-supersymmetric Seiberg duality. After level shifts from loop effects, this identifies the IR of Sp(2N)_{2k-2N+2} and Sp(2k-2N+2)_{-2N} pure Chern-Simons theories, which is a level-rank pair. We also derive level-rank duality in a Chern-Simons theory based on a unitary group.
We discuss how to incorporate non-supersymmetric branes in compactifications of type II string theories. We particularly focus on flux compactifications on $SU(3)\times SU(3)$ structure manifolds to four dimensions, so that a linear $\mathcal{N}=1$ supersymmetry is spontaneously broken by spacetime filling Dp-branes. Anti-Dp-branes are a very special subset of such branes but our analysis is generic. We show that the backreaction of non-supersymmetric branes can be incorporated into the standard 4d $\mathcal{N}=1$ supergravity by including a nilpotent chiral multiplet. Supersymmetry in such se…
We obtain new examples of partially supersymmetric M-brane solutions defined on products of Ricci-flat manifolds, which contain two-dimensional Lorentzian submanifold R^{1,1}_{*}/Z_2 with one parallel spinor. The examples belong to the following configurations: M2, M5, M2-M5 and M5-M5. Among them a M2 solution with N =1/32 fractional number of preserved supersymmetries is presented. The examples with three M-branes were considered earlier in our paper with A.A. Golubtsova.
We consider genuine type IIB string theory (supersymmetric) brane intersections that preserve $(1+1)$D Lorentz symmetry. We provide the full supergravity solutions in their analytic form and discuss their physical properties. The Ansatz for the spacetime dependence of the different brane warp factors goes beyond the harmonic superposition principle. By studying the associated near-horizon geometry, we construct interesting classes of AdS$_3$ vacua in type IIB and highlight their relation to the existing classifications in the literature. Finally, we discuss their holographic properties.
We discuss non-linear instantons in supersymmetric field theories on curved spaces arising from D-branes. Focusing on D3-branes and four-dimensional field theories, we derive the supersymmetry conditions and show the intimate relation between the instanton solutions and the non-linearly realized supersymmetries of the field theory. We demonstrate that field theories with non-linearly realized supersymmetries are coupled to supergravity backgrounds in a similar fashion as those with linearly realized supersymmetries, and provide details on how to derive such couplings from a type II perspective…
We construct novel $7d$ supersymmetric gauge theories which include a Chern-Simons-like term on curved spaces. In order to so, we examine the supersymmetry constraints for E7-branes in type IIA$^*$ theory, rather than making use of an off-shell supergravity. We find two classes of solutions to the constraints, expressed in terms of a $G_2$-structure with non-vanishing intrinsic torsion. The supersymmetric gauge theories are then obtained by coupling flat gauge theory to such supersymmetric backgrounds. Various examples are given, including round and squashed $S^7$ as well as $S^3 \times M_4$ w…
