Related papers: Renormalization for holomorphic field theories
A family of connections on the space of couplings for a renormalizable field theory is defined. The connections are obtained from a Levi-Civita connection, for a metric which is a generalisation of the Zamolodchikov metric in two…
We perform a holographic renormalization of cascading gauge theories. Specifically, we find the counter-terms that need to be added to the gravitational action of the backgrounds dual to the cascading theory of Klebanov and Tseytlin,…
Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
Holomorphy of the superpotential and of the coefficient of the gauge kinetic terms in supersymmetric theories lead to powerful results. They are the underlying conceptual reason for the important non-renormalization theorems. They also…
The density matrix renormalization group is applied to a relativistic complex scalar field at finite chemical potential. The two-point function and various bulk quantities are studied. It is seen that bulk quantities do not change with the…
Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…
We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has relatively few orbits? We prove that any field which has only…
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV)…
We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous Konig's Theorem and Bottcher's Theorem in classical complex…
Several field theoretical approaches to the superconducting phase transition are discussed. Emphasis is given to theories of scaling and renormalization group in the context of the Ginzburg-Landau theory and its variants. Also discussed is…
A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit theory yields the global averages characterizing the chaotic…
We study the renormalizability in theories of a self-interacting Lifshitz scalar field. We show that although the statement of power-counting is true at one-loop order, in generic cases where the scalar field is dimensionless, an infinite…
This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for…
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a field theoretic renormalization group. The environment motion is modelled by the stochastic Navier--Stokes equation, which includes…
We consider deformations of a conformal field theory that explicitly break some global symmetries of the theory. If the deformed theory is still a conformal field theory, one can exploit the constraints put by conformal symmetry to compute…
Elaborating on our previous presentation, where the term {\it dipolar quantization} was introduced, we argue here that adopting $L_0-(L_1+L_{-1})/2+{\bar L}_0-({\bar L}_1+{\bar L}_{-1})/2$ as the Hamiltonian instead of $L_0+{\bar L}_0$…