Related papers: A Note on AdS/SYM Correspondence on the Coulomb Br…
This is an introduction to the Maldacena conjecture on the equivalence between ${\cal{N}}=4$ super Yang-Mills in Minkowski space-time and type IIB string theory compactified on $AdS_5 \otimes S_5 $.
We show that Coulomb branches for $3$-dimensional $\mathcal{N}=4$ supersymmetric gauge theories have symplectic singularities. This confirms a conjecture of Braverman-Finkelberg-Nakajima.
We compute certain two-point functions in D=4, ${\cal N}=4$, SU(N) SYM theory on the Coulomb branch using SUGRA/SYM duality and find an infinite set of first order poles at masses of order $({\rm Higgs~scale})/(g_{YM} \sqrt{N})$.
We report on a test of the Maldacena conjecture. This string/field theory correspondence has interesting applications. When combined with Rehren's theorem, it has implications for issues concerning space-time structure and Lorentz symmetry.…
In this paper, we investigate the twisted $A_{2n}$ sector of class-S theories. Heretofore, the Coulomb branches of such theories have been poorly understood. In this, and a companion paper, we make progress in our understanding of them. In…
This dissertation consists of a comprehensive and pedagogical review of Maldacena's original derivation of the AdS/CFT correspondence and the main topics of string theory necessary to understand it. The large $N$ expansion of Yang-Mills…
Symplectic resolutions are an exciting new frontier of research in representation theory. One of the most fascinating aspects of this study is symplectic duality: the observation that these resolutions come in pairs with matching…
We generalize the Maldacena correspondence to the logarithmic conformal field theories. We study the correspondence between field theories in (d+1)-dimensional AdS space and the d-dimensional logarithmic conformal field theories in the…
A U(2,2|4)-invariant A-model constructed from fermionic superfields has recently been proposed as a sigma model for the superstring on AdS_5xS^5. After explaining the relation of this A-model with the pure spinor formalism, the A-model…
This expository article discusses recent advances in understanding 3-dimensional mirror symmetry and the mathematical definitions of the Higgs and Coulomb branches. This is a slightly expanded version of an article appearing in the Notices…
In the present paper we study SU(N)->S(U(N/2)xU(N/2)) symmetry breaking in N=4 SYM via AdS/CFT correspondence. We consider two stacks of N/2 parallel D3 branes separated by a distance 2\vec d. In this case there is mixing between the…
These are (somewhat informal) lectures notes for the CIME summer school "Geometric Representation Theory and Gauge Theory" in June 2018. In these notes we review the results and constructions of a series of our joint papers with H.Nakajima…
The theory of secondary chomology operations leads to a conjecture concerning the algebra of higher cohomology operations in general. This conjecture is discussed here in detail and its connection with homotopy groups of spheres and the…
These lectures do not at all provide a general review of this rapidly growing field. Instead a rather detailed account is presented of a number of the most elementary aspects.
We study (4,4) supersymmetric field theories in two dimensions with a one dimensional Coulomb branch. These theories have applications in string theory. Our analysis explains the known relation between $A-D-E$ groups and modular invariants…
The Adams conjecture predicts that the local theta correspondence should respect Arthur packets. In this paper, we revisit the Adams conjecture for the symplectic--even orthogonal dual pair. Our results provide a precise description of all…
The study of Coulomb branches of 3-dimensional N=4 gauge theories via the associated Hilbert series, the so-called monopole formula, has been proven useful not only for 3-dimensional theories, but also for Higgs branches of 5 and…
A relation between confinement and Maldacena conjecture is briefly discussed. The gauge symmetry enhancement for two coincident D-6-branes is analyzed from the viewpoint of the hypermultiplet low-energy effective action given by the N=2…
Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we present a correspondence between networks of small resolutions for singular elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge theories. While…
An elementary introduction to Maldacena's AdS/CFT correspondence is given, with some emphasis in the Fefferman-Graham construction. This is based on lectures given by one of us (E.A.) at the Universidad Autonoma de Madrid.