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Strange horizons

The gauge/gravity duality, also known as the AdS/CFT correspondence or holography, relates quantum field theories to theories of quantum gravity in one dimension higher. When one theory is strongly coupled, and therefore very difficult to study directly, the other one is weakly coupled. In this thesis, we will use this duality to study a variety of physical phenomena in strongly coupled quantum field theories by performing computations in their weakly coupled gravitational duals.

After reviewing the gauge/gravity duality in the first part, we discuss various aspects of non-conformal holography in part II. We construct new solutions of ten-dimensional type II supergravity which describe the back-reaction of Dp-branes, for 1 =< p =< 6, with a spherical worldvolume. These solutions are holographically dual to maximally supersymmetric Yang-Mills (SYM) theory on a (p +1)-dimensional sphere, Sp+1. The finite size of the sphere provides a IR cut-off in the gauge theory, which is reflected in the dual geometry as a smooth cap-off. In the UV, the size of the sphere plays no role and our solutions asymptote to the well-known supergravity backgrounds describing the near-horizon limit of flat Dp-branes. Using these solutions we can holographically compute the free energy and 1/2-BPS Wilson loop vacuum expectation values in the dual gauge theory. Using supersymmetric localization, we can perform the same computation directly in planar maximal SYM theory on the (p+1)-sphere at strong coupling. We find excellent agreement between the two sets of results for all values of p. This constitutes a highly non-trivial precision test of holography in a non-conformal setting.

In part III we study a class of AdSp solutions of type II supergravity which describe the IR dynamics of p-branes wrapped on a Riemann surface. Such solutions are
classified by solutions of the Liouville equation. Regular solutions lead to well-known wrapped brane supergravity solutions with the constant curvature metric on the Riemann surface. We show that singular solutions of the Liouville also have a physical interpretation as explicit point-like brane sources on the Riemann surface. These supergravity solutions are dual to strongly coupled (p + 1)-dimensional conformal field theories obtained as the IR fixed point of a renormalization group flow across dimensions starting in p + 1 dimensions. These theories are strongly coupled and extremely hard to access using purely field theoretical methods. We test the details of our proposal by focusing on N = 1 superconformal field theories of class S, arising from M5-branes wrapped on a punctured Riemann surface. We present explicitly the dual AdS5 solutions and check the proposed duality by finding non-trivial agreement of the ’t Hooft anomalies, the dimension of the conformal manifold and the conformal dimensions of various operators in the theory with their holographic duals.

Date:1 Oct 2016 →  23 Jun 2020
Keywords:Quantum field theory, String theory, Supergravity, Holography
Disciplines:Field theory and string theory, Applied mathematics in specific fields, Quantum physics, Mathematical physics
Project type:PhD project