Related papers: Conformal Invariance = Finiteness and Beta Deforme…
The construction of supersymmetric invariant integrals is discussed in a superspace setting. The formalism is applied to D=4, N=4 SYM and used to construct the F^2, F^4 and (F^5 + \del^2 F^4) terms in the effective action of coincident…
We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…
The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical…
We reformulate the Omega-deformation of four-dimensional gauge theory in a way that is valid away from fixed points of the associated group action. We use this reformulation together with the theory of coisotropic A-branes to explain recent…
We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed $\mathcal{N}=4$ SYM theory. We show…
We calculate the renormalization constants of the maximally extended N=4 supersymmetric Yang-Mills theories in the dimensional reduction scheme up to four loops. We have found, that the beta-function is zero both from gauge and Yukawa…
As it stands, quantum gravity coupled with matter in three spacetime dimensions is not finite. In this paper I show that an algorithmic procedure that makes it finite exists, under certain conditions. To achieve this result, gravity is…
We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators…
We constructed the most general N=4 superconformal 3-particles systems with translation invariance. In the basis with decoupled center of mass the supercharges and Hamiltonian possess one arbitrary function which defines all potential…
An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for…
The de Finetti theorem and its extensions concern the structure of multipartite probability distributions with certain symmetry properties, the paradigmatic original example being permutation symmetry. These theorems assert that such…
We consider the twisted N = 4 SYM on \Sigma \times S^2. In the limit that S^2 shrinks to zero size the four dimensional theory reduces to a two dimensional SYM theory. We compute the correlation functions of a set of BRST cohomology classes…
We analyse the phase structure of an $\mathcal{N}=2$ massive deformation of $\mathcal{N}=4$ SYM theory on an four-dimensional ellipsoid using recent results on supersymmetric localisation. Besides the 't~Hooft coupling $\lambda$, the…
A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the…
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.
The vacuum sector of the Brans-Dicke theory is studied from the viewpoint of a non-conformally invariant gravitational model. We show that, this theory can be conformally symmetrized using an appropriate conformal transformation. The…
Quantum field theories with exact but spontaneously broken conformal invariance have an intriguing feature: their vacuum energy (cosmological constant) is equal to zero. Up to now, the only known ultraviolet complete theories where…
The properties of gauge-invariant composite operators and their correlation functions in N=4 SYM are discussed in the analytic superspace formalism. A complete classification of the different types of operators in the theory is given.…
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the…
It is argued that dimensional reduction of Seiberg-Witten map for a gauge field induces Seiberg-Witten maps for the other noncommutative fields of a gauge invariant theory. We demonstrate this observation by dimensionally reducing the…