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Dvali and Shifman have proposed a field-theoretic mechanism for localizing gauge fields to "branes" in higher dimensional spaces using confinement in a bulk gauge theory. The resulting objects have a number of qualitative features in common…
Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N. In this paper, we compute the scaling dimensions of…
It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be…
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the…
Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), $T_{3,{3\over2}}$, emerging in this duality splits…
We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI…
We review recent developments in the study of the AdS/CFT correspondence in lower dimensions. We start summarising the classification of AdS$_3\times$S$^2$ solutions in massive Type IIA supergravity with (0,4) supersymmetries, and the…
The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…
Recent progress towards understanding a strong coupling expansion for various superconformal field theories in four dimensions is described. First, the case of the maximally supersymmetric Yang Mills theory is analyzed, as well as many…
We study issues of duality in 3D field theory models over a canonical noncommutative spacetime and obtain the noncommutative extension of the Self-Dual model induced by the Seiberg-Witten map. We apply the dual projection technique to…
We propose a duality between the 2d W_N minimal models in the large N 't Hooft limit, and a family of higher spin theories on AdS_3. The 2d CFTs can be described as WZW coset models, and include, for N=2, the usual Virasoro unitary series.…
We classify ${\cal N}=1$ gauge theories with simple gauge groups in four dimensions which possess a conformal manifold passing through weak coupling. A very rich variety of models is found once one allows for arbitrary representations under…
We present M-theory compactifications on $K_3 \times K_3$ with membranes near the $A_n$ or $D_n$ singularities of the $K_3$ spaces. By realizing each of these compactifications in two different ways as type I' models with 2- and 6-branes,…
The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well…
We study baryons in an AdS/CFT model of QCD by Sakai and Sugimoto, realized as small instantons with fundamental string hairs. We introduce an effective field theory of the baryons in the five-dimensional setting, and show that the…
We derive D-brane gauge theories for C^3/Z_n x Z_n orbifolds with discrete torsion and study the moduli space of a D-brane at a point. We show that, as suggested in previous work, closed string moduli do not fully resolve the singularity,…
The low-energy description of wrapped M5 branes in compactifications of M-theory on a Calabi-Yau threefold times a circle is given by a conformal field theory studied by Maldacena, Strominger and Witten and known as the MSW CFT. Taking the…
We review M-theory description of 4d N=2 SQCD. Configurations of M-theory fivebranes relevant to describe the moduli spaces of the Coulomb and Higgs branches are studied using the Taub-NUT geometry. Minimal area membranes related with the…
We study the global geometry of a general class of spacetimes of relevance to the supersymmetric $AdS_3/CFT_2$ correspondence in eleven-dimensional supergravity. Specifically, we study spacetimes admitting a globally-defined…
This thesis is devoted to derivative corrections to the effective action of D-branes, and to mirror symmetry with D-branes. Series of derivative corrections first predicted by non-commutative gauge theory are completed by couplings between…