Related papers: Conformal quantum field theory in various dimensio…
Correlation functions in Euclidean conformal field theories in four dimensions are expressed as representations of the conformal group $SL(2,\H)$, $\H$ being the field of quaternions, on the configuration space of points. The…
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell closed string states. The dynamic equation corresponding to the condition of conformal invariance includes an infinite number…
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum…
A path-integral method effective beyond the perturbation expansion approach is suggested to consider the quartic anharmonicity in different spatial dimensions. Due to an optimal representation of the partition function, the leading term has…
We investigate domain-wall/quantum field theory correspondences in various dimensions. Our general analysis does not only cover the well-studied cases in ten and eleven dimensions but also enables us to discuss new cases like a Type…
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of…
Conformal field theory (CFT) in two dimensions provide a rich source of subfactors. The fact that there are so many subfactors coming from CFT have led people to conjecture that perhaps all finite depth subfactors are related to CFT. In…
We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with $1\leq Q\leq 4$. We check that the usually invoked correspondence between FK clusters…
We show that 4--dimensional conformal field theory is most naturally formulated on Kulkarni 4--folds, i. e. real 4--folds endowed with an integrable quaternionic structure. This leads to a formalism that parallels very closely that of…
I explain the motivation for investigating the high energy limit of QCD and give a brief presentation of recent progress in the understanding of unitarity corrections in this kinematic regime. Special emphasis is given to the conformal…
A unified field theory in ten dimensions, of all interactions, can describe high energy processes occuring in the early universe. In such a theory transitions that give properties of the universe can occur due to the presence of algebraic…
We study 1+1-dimensional theories of vector and hypermultiplets with (4,4) supersymmetry. Despite strong infrared fluctuations, these theories flow in general to distinct conformal field theories on the Coulomb and Higgs branches. In some…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
We introduce and study a new 3d Topological Field Theory which can be associated to any compact real manifold X. This TFT is analogous to the 2d A-model and reduces to it upon compactification on an interval with suitable boundary…
This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…
Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
I show that a particle structure in conformal field theory is incompatible with interactions. As a substitute one has particle-like exitations whose interpolating fields have in addition to their canonical dimension an anomalous…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…