[en] We suggest that orbifold field theories which are obtained from non-commutative N=4 SYM are UV finite. In particular, non-supersymmetric orbifold truncations might be finite even at finite values of Nc. (author)

[en] A factorized substraction formula for R-operation is discussed. The notion of T-diagrams as a special class of Feynmann diagrams is introduced. For T-diagrams the factorized renormalization formula is shown to be reducible to Zimmermann's forest formula for R-operation. 10 refs. (author)

[en] One-loop divergences appearing in the entropy of a quantum black hole are proven to be completely eliminated by the standard renormalization of both the gravitational constant and other coefficients by the R²-terms in the effective gravitational action. The essential point of the proof is that due to the higher order curvature terms the entropy differs from the Bekenstein-Hawking one in the Einstein gravity by the contributions depending on the internal and external geometry of the horizon surface. 15 refs

[en] We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur

[en] The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.

[en] Analyzing general renormalization constants in covariant gauge and minimal subtraction, we consider universal conditions for cancelling UV-divergences in renormalizable field theories with simple gauge groups, and give constructive methods for finding nonsupersymmetric finite models. The divergent parts of the renormalization constants for fields explicitly depend on the gauge parameter ξ. Finite theories simply need finite couplings. We show that respective FinitenessConditions imply a hierarchy, the center of which are the FCs for the gauge coupling g and the Yukawa couplings of the massless theory. To gain more information about F we analyze the Yukawa-FC in greater detail. Doing so algebraically, we find out and fix all inner symmetries. Additionally, Yuakawa-couplings must be invariant under gauge transformation. Then it becomes extremely difficult to obey a FC, yield rational numbers for F ∼ 1, and satisfy the factorization-condition, unless F = 1. The particular structure of the F = 1-system allows for a most general ansatz. We figure out the simplest case, getting precisely just couplings and particle content of a general N=1-supersymmetric theory. We list a class of roughly 4000 types of theories, containing all supersymmetric, completely finite, and many more finite theories as well. (Author, shortened by Quittner) 11 figs., 54 refs

[en] This review contains a detailed description of methods of calculating ultraviolet divergences in two-dimensional nonlinear theories. The basic notions of the geometry of Riemannian manifolds are given, and the concept of the generalized renormalizability of sigma models is introduced. The covariant background-field method in nonlinear theories is described. The problem of infrared divergences and methods of removing them are discussed. The methods are illustrated by two-loop calculations in bosonic sigma models with the Wess-Zumino term and by four- and five-loop calculations in N=1 and N=2 supersymmetric sigma models. The role of Ricci-flat manifolds in obtaining conformally invariant sigma models is discussed in the concluding section. 72 refs., 9 figs., 2 tabs

[en] Some of nature’s rhymes—the appearance of similar structures in different areas of physics—underlie the way that string theory potentially unifies gravity with the other forces of nature and eliminates the ultraviolet divergences that plague quantum gravity.

[en] We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur

[en] The generic Feynman amplitude for a graph G, defined in an earlier paper by an integral over Feynman parameters, is itself a function of regularizing parameters, lambda, ν. The desingularization of the integral which is needed to exhibit the meromorphic structure in these variables is worked out. All ultraviolet and infrared singularities are determined, and these are shown to correspond to certain types of sub and quotient graphs of G, respectively