Related papers: On Certain Two Dimensional Integrals that Appear I…
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is…
Finding upper and lower bounds to integrals with respect to copulas is a quite prominent problem in applied probability. In their 2014 paper, Hofer and Iaco showed how particular two dimensional copulas are related to optimal solutions of…
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory. We provide exact, finite-coupling…
I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: i) central…
The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we…
We obtain by superfield methods the exceptional representations of the OSp(2N/4,R) and SU(2,2/1) superalgebras which extend to supersingletons of SU(2,2/2N) and F(4), respectively. These representations describe superconformally coupled…
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…
We analyze the topology and geometry of a polyhedron of dimension 2 according to the minimum size of a cover by PL collapsible polyhedra. We provide partial characterizations of the polyhedra of dimension 2 that can be decomposed as the…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
We argue that rational conformally invariant quantum field theories in two dimensions are closely related to torsion elements of the algebraic K-theory group K_3(C). If such a theory has an integrable matrix perturbation with purely elastic…
We investigate anisotropic conformal Carroll field theories and their holographic duals. On the field theory side, we focus on the case with scaling exponent $z=0$ in two and three spacetime dimensions. These theories exhibit…
We construct an integral model of the perfectoid modular curve. Studying this object, we prove some vanishing results for the coherent cohomology at perfectoid level. We use a local duality theorem at finite level to compute duals for the…
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the…
This thesis explores the correspondence between Chern-Simons theory and integrable field theories across different dimensions. It brings together all of my work in this area, including several distinct realizations of this correspondence.…