Title:

Aspects of the class S superconformal index, and gauge/gravity duality in five/six dimensions

In the first part of this thesis, we discuss some aspects of the fourdimensional N = 2 superconformal index of theories of class S. We first consider a generalized index on S^{1} × S^{3}/Z_{r}, and prove Sduality in a particular fugacity slice. We then go on to study the (round) superconformal index in the presence of surface defects. We develop a systematic prescription to compute surface defects labeled by arbitrary irreducible representations of the gauge group and subject those defects to various tests in several different limits. Each of these limits is interesting in its own right, and we go on to explore them in some depth. In the second part of this thesis, we construct the gravity duals of large N supersymmetric gauge theories defined on squashed fivespheres with SU(3) × U(1) symmetry. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplift to massive type IIA supergravity. We compute the partition function and Wilson loop in the large N limit of the gauge theory and compare them to their corresponding supergravity dual quantities. As expected from AdS/CFT, both sides agree perfectly. Based on these results, we conjecture a general formula for the partition function and Wilson loop on any fivesphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector. We then go on to construct rigid supersymmetric gauge theories on more general Riemannian fivemanifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of the sixdimensional bulk supergravity solution. This leads to a systematic classification of fivedimensional supersymmetric backgrounds with gravity duals.
