Three dimensional quantum field theories provide a nice testing grounds for exploring quantum field theory phenomena. Very simple UV theories can have highly nontrivial, and rich IR dynamics. These lectures will give a pedagogical review of various aspects of quantum field theory, including instantons, monopoles, the conformal window, vortices, skyrmions, Chern-Simons terms, etc., in the context of 3d quantum field theories. In the context of susy theories, we will review older work on exact results, mirror symmetry and duality, and also mention some more recent results.

Three dimensional quantum field theories provide a nice testing grounds for exploring quantum field theory phenomena. Very simple UV theories can have highly nontrivial, and rich IR dynamics. These lectures will give a pedagogical review of various aspects of quantum field theory, including instantons, monopoles, the conformal window, vortices, skyrmions, Chern-Simons terms, etc., in the context of 3d quantum field theories. In the context of susy theories, we will review older work on exact results, mirror symmetry and duality, and also mention some more recent results.

Three dimensional quantum field theories provide a nice testing grounds for exploring quantum field theory phenomena. Very simple UV theories can have highly nontrivial, and rich IR dynamics. These lectures will give a pedagogical review of various aspects of quantum field theory, including instantons, monopoles, the conformal window, vortices, skyrmions, Chern-Simons terms, etc., in the context of 3d quantum field theories. In the context of susy theories, we will review older work on exact results, mirror symmetry and duality, and also mention some more recent results.

QMUL Graduate Lectures

Abstract: Within the context of the AdS4/CFT3 correspondence I will present recent results concerning the evaluation of scattering amplitudes for N=6 Chern-Simons-matter theories. I will discuss their peculiar properties like dualities, symmetries and exponentiation.

QMUL Graduate Lectures

QMUL Graduate Lectures

We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave expansion in Mellin space, elucidating the analytic structure of the partial amplitudes. We apply the new formalism to the case of four point correlation functions between protected scalar operators in N=4 Super Yang Mills, in cases where the Regge limit is controlled by the leading twist operators associated to the pomeron-graviton Regge trajectory. At weak coupling, we are able to predict to arbitrary high order in the 't Hooft coupling the behaviour near J=1 of the OPE coefficients C_{OOJ} between the external scalars and the spin J leading twist operators. At strong coupling, we use recent results for the anomalous dimension of the leading twist operators to improve current knowledge of the AdS graviton Regge trajectory - in particular, determining the next and next to next leading order corrections to the intercept. Finally, by taking the flat space limit and considering the Virasoro-Shapiro S-matrix element, we compute the strong coupling limit of the OPE coefficient C_{LLJ} between two Lagrangians and the leading twist operators of spin J.

Abstract: In the AdS/CFT correspondence, gauge theory calculations beyond the planar approximation correspond to quantum corrections in gravity or in string theory. Recently, the partition function on the three-sphere of Chern-Simons-matter theories has been computed at all orders in the 1/N expansion, and this leads to predictions for quantum corrections in M-theory/string theory. Using the ideas of effective field theory, we show that some of these corrections can be calculated reliably by doing one-loop calculations in supergravity. A similar reasoning has been used recently to calculate logarithmic corrections to black hole entropy, and we use it here to perform a successful test of AdS_4/CFT_3 beyond the leading, planar approximation.

A pedagogical introduction to the Regge limit of scattering amplitudes will be given. Its role in collider physics will be explained, together with its connections to integrability in QCD and SUSY theories. We will finish with a discussion on graviton scattering at high energies.

I will explain how the notion of T-duality can be generalised to the case of a non-abelian isometry group and applied as a solution generating symmetry to type II supergravity backgrounds involving RR flux. I will show some novel mappings between IIB and (massive) IIA supergravity and apply the technique to backgrounds of importance in the context of the gauge/gravity correspondence. In particular we will find some surprising connections between $AdS_5\times S^5$ and the geometry proposed by Gaiotto and Maldacena as dual to certain N=2 SCFT's and between the Klebanov-Witten background ($AdS_5 \times T^{1,1}$) and the geometries discussed already in this seminar series by Wecht as dual to certain N=1 SCFT's. Time permitting I will describe some recent developments relating to the gravity duals of cascading gauge theories.

We use an observation of Maldacena to argue that gravity tree-amplitudes can be computed by inserting appropriate wave-functions into the Witten-Berkovits twistor-string for conformal gravity. This is used to motivate and partially explain the recent remarkable twistor-string-like formula of Cachazo & Skinner that expresses the complete tree-level S-matrix for N=8 supergravity in terms of an integral over rational curves in twistor space.

I will describe a new infinite set of AdS/CFT dual pairs which come from M5-branes wrapping Riemann surfaces. These solutions interpolate between and extend beyond a famous pair of solutions by Maldacena and Nunez. Additionally, the dual SCFTs are so-called "non-Lagrangian" theories, which have no weakly coupled UV description yet can (and will) be described explicitly.