相关论文: Irregular conformal blocks, Painlev\'e III and the…

We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings. The construction of such mappings comes from our construction of non-trivial compact…

We consider the semilinear wave equation in the radial case with conformal subcritical power nonlinearity. If we consider a blow-up point different from the origin, then we exhibit a new Lyapunov functional which is a perturbation of the…

In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the $\mathcal{N}=4$ super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling…

We investigate the perturbative renormalisation of deformed conformal field theories from the Hamiltonian perspective. We discuss the relation with conformal perturbation theory, to which we provide an explicit match up to third order in…

Using supersymmetric localization, we consider four-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained from $\mathbb{Z}_n$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling.…

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…

We study the analytic structure of semiclassical conformal blocks, namely of the 1-point conformal block on the torus and of the 4-point conformal block on the sphere, as functions of the intermediate dimension. We interpret their…

In this thesis we investigate the effective actions for massive Kaluza-Klein states, focusing on the massive modes of spin-3/2 and spin-2 fields. To this end we determine the spontaneously broken gauge symmetries associated to these `higher…

In recent years, the Fourier series (Zak transform) structure of the Painlev\'e I tau function has emerged in multiple contexts. Its main building block admits several conjectural interpretations, such as the partition function of an…

Virasoro conformal blocks are universal ingredients of correlation functions of two-dimensional conformal field theories (2d CFTs) with Virasoro symmetry. It is acknowledged that in the (classical) limit of large central charge of the…

We obtain the complete superconformal symmetry transformations on the worldvolume of a D3-brane in an $AdS_5\times S^5$ background by using a coset superspace approach. We show that in the large $R$-limit we recover all supersymmetries…

We explore the proposal that the six-dimensional (2,0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated N=2 superconformal theories of Argyres-Douglas type, and to…

We study the linear problems in $z,t$ (time) associated to the Painlev\'e III$_3$ and III$_1$ equations when the Painlev\'e solution $q(t)$ approaches a pole or a zero. In this limit the problem in $z$ for the Painlev\'e III$_3$ reduces to…

The dilute A_3 model is a solvable IRF (interaction round a face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A_3. It can be regarded as a solvable version of an Ising model at the…

Some new Hamiltonian systems of quasi-Painlev\'e type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlev\'e…

We build the Z$_{3}$ invariants fusion rules associated to the (D$_{4}$,A$_{6}$) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-pt correlation functions of critical fields are developed in the…

We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point…

We study the dual descriptions recently discovered for the Seiberg-Witten theory in the presence of surface operators. The Nekrasov partition function for a four-dimensional N=2 gauge theory with a surface operator is believed equal to the…

The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…

In this outline of a program, based on rigorous renormalization group theory, we introduce new definitions which allow one to formulate precise mathematical conjectures related to conformal invariance as studied by physicists in the area…