Related papers: The Small ${\cal N}=4$ Superconformal ${\cal W}_{\…

In this paper we review aspects of anti de Sitter/conformal field theory (AdS/CFT) duality and the notion of holographic renormalization group (RG) flow. We start by discussing supersymmetry and construct the N = 4 super Yang-Mills theory…

We discuss an orbifold of the toroidally compactified heterotic string which gives a global reduction of the dimension of the moduli space while preserving the supersymmetry. This construction yields the moduli space of the first of a…

We conjecture the Quantum Spectral Curve equations for string theory on $AdS_3 \times S^3 \times T^4$ with RR charge and its CFT$_2$ dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the…

We propose a mirror symmetry for 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator algebra (VOA) describing the Schur sector (containing Higgs…

The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de…

We construct and study the supersymmetry properties of the weighted projective spaces $\mathbb{WCP}^2$ and $\mathbb{WCP}^3$. These are topologically $\mathbb{CP}^n$ with $n+1$ orbifold singularities and as such are higher dimensional…

We define a holographic dual to the Donaldson-Witten topological twist of $\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$ gauged…

We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then…

We construct an exact metric which at short distances is the metric of massless particles in 5+1 spacetime (moving along a diameter of the sphere) and is AdS_3\times S^3 at infinity. We also consider a set of a conical defect spacetimes…

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 give a characterisation of representation-finite symmetric algebras of period four, and describe their basic algebras. In particular, if such an algebra is indecomposable, it has at most two simple modules.

We propose a novel string theory propagating in a non-commutative deformation of the four dimensional space T* T^2 whose scattering states correspond to superconformal theories in 5 dimensions and the scattering amplitudes compute…

We carry out an exact worldsheet computation of tree level three-point correlators of chiral operators in string theory on AdS(3) x S^3 x T^4 with NS-NS flux. We present a simple representation for the string chiral operators in the…

The holographic duals of higher spin theories on AdS_3 are described by the large N limit of a family of minimal model CFTs, whose symmetry algebra is equivalent to W(infinity)[lambda]. We study perturbations of these limit theories, and…

Suppose N is an affine SL(2,R)-invariant submanfold of the moduli space of pairs (M,w) where M is a curve, and w is a holomorphic 1-form on M. We show that the Forni bundle of N (i.e. the maximal SL(2,R)-invariant isometric subbundle of the…

Two and three-point functions of primary fields in four dimensional CFT have a simple space-time dependences factored out from the combinatoric structure which enumerates the fields and gives their couplings. This has led to the formulation…

It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D) ${\mathcal N}=2\;$ supersymmetric QCD (SQCD) with the U($N=2$) gauge group and $N_f=4$ quark flavors behave as critical superstrings. In addition…

We propose an electric-magnetic duality and conjecture an exact conformal window for a class of non-supersymmetric U(N_c) gauge theories with fermions in the (anti)symmetric representation of the gauge group and N_f additional scalar and…

The AdS(4)/CFT(3) duality is a new example of an integrable and exactly solvable AdS/CFT system. There is, however, a puzzling mismatch between the number of degrees of freedom used in the exact solution (4B+4F scattering states) and 8B+8F…

It was recently proposed that a large N limit of a family of minimal model CFTs is dual to a certain higher spin gravity theory in AdS_3, where the 't Hooft coupling constant of the CFT is related to a deformation parameter of the higher…