Exact results in the gauge/gravity duality

• Main Author: Lorenzen, Jakob Christian
• Other Authors: Gromov, Nikolay ; Martelli, Dario
• Published: King's College London (University of London) 2016
• Subjects: 530.14
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.686373

In this thesis we study the gauge/gravity duality and exact results in supersymmetric quantum field theories obtained using localization. We construct the gravity duals to a broad class of N = 2 supersymmetric gauge theories defined on a general class of three-manifolds. The gravity backgrounds are supersymmetric solutions of gauged four-dimensional supergravity and encompass all known examples of such solutions. We find that the holographically renormalized on-shell action agrees with the free energy of the field theory, which has previously been computed via localization of the partition function. Next, we study the Casimir energy of four-dimensional N = 1 supersymmetric field theories in the context of the rigid limit of new minimal supergravity. We revisit the computation of the localized partition function on S1 S3, and consider the same theories in the Hamiltonian formalism on R S3. We compute the vacuum expectation value of the canonical Hamiltonian using zeta function regularization, and show that this interpolates between the supersymmetric Casimir energy and the ordinary Casimir energy of supersymmetric field theories. In general, the Casimir energy depends on the regularization scheme and is therefore ambiguous. However, we show that for N = 1 supersymmetric field theories on the cylinder R S3, the supersymmetric Casimir energy is well-defined and scheme-independent, provided the regularization scheme preserves supersymmetry. Finally, we investigate the gravity duals of such N = 1 theories on R S3. Specifically, we study supersymmetric solutions of five-dimensional minimal gauged supergravity using a known classification. We propose an ansatz based on a four-dimensional local orthotic Kahler metric and reduce the problem to a single sixth-order equation for two functions, each of one variable. We find an analytic, asymptotically locally AdS solution comprising five parameters. For a conformally at boundary, this reduces to a previously known solution with three parameters, representing the most general solution of this type known in minimal gauged supergravity. We discuss the relevance for this solution to account for the supersymmetric Casimir energy, finding the answer to be in the negative.