The relation between the trace and R-current anomalies in supersymmetric theories implies that U$(1)_RF^2$, U$(1)_R$ U$(1)_R^3$ which are matched studies of N=1 Seiberg duality satisfy positivity constraints. Some constraints rigorous others conjectured as four-dimensional generalizations Zamolodchikov $c$-theorem. These tested a large number gauge non-Abelian Coulomb phase, they satisfied all renormalizable models with unique anomaly-free R-current, including those accidental symmetry. Most...

We study the main options for a unitary and renormalizable, local quantum field theory of gravitational interactions. The first model is Lee-Wick superrenormalizable higher-derivative gravity, formulated as nonanalytically Wick rotated Euclidean theory. show that, under certain conditions, $S$ matrix when cosmological constant vanishes. simplest its class. However, infinitely many similar are allowed, which raises issue uniqueness. To deal with this problem, we propose new quantization...

The Lee-Wick models are higher-derivative theories that claimed to be unitary thanks a peculiar cancelation mechanism. In this paper, we provide new formulation of the models, clarify several aspects have remained quite mysterious, so far. Specifically, define them as nonanalytically Wick rotated Euclidean theories. complex energy plane is divided into disconnected regions, which can related one another by well-defined, albeit nonanalytic procedure. Working in generic Lorentz frame,...

We study the perturbative unitarity of Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions and values a loop integral in various are related to one another by nonanalytic procedure. show that one-loop diagrams satisfy expected, unitary cutting equations each region: only physical d.o.f. propagate through cuts. goal can be achieved working suitable subsets region proving analytically continued whole....

We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving behavior Feynman diagrams by means higher space derivatives. Higher time derivatives are not generated renormalization. Renormalizability is ensured a ``weighted power-counting'' criterion. The contain dimensionful parameter ${\ensuremath{\Lambda}}_{L}$, yet set models classically invariant under weighted scale transformation, which anomalous at level....

The "fakeon" is a fake degree of freedom, i.e. freedom that does not belong to the physical spectrum, but propagates inside Feynman diagrams. Fakeons can be used make higher-derivative theories unitary. Moreover, they help us clarify how Lee-Wick models work. In this paper we study fakeon models, say contain and degrees freedom. We formulate them by (nonanalytically) Wick rotating their Euclidean versions. investigate properties arbitrary diagrams and, among other things, prove are...

We elaborate on the idea of fake particle and study its physical consequences. When a theory contains fakeons, true classical limit is determined by quantization subsequent process "classicization". One major predictions due to particles violation microcausality, which survives limit. This fact gives hope detect experimentally. A fakeon spin 2, together with scalar field, able make quantum gravity renormalizable while preserving unitarity. claim that emerging from this construction right...

We investigate the properties of fakeons in quantum gravity at one loop. The theory is described by a graviton multiplet, which contains fluctuation $h_{\mu \nu }$ metric, massive scalar $\phi $ and spin-2 fakeon $\chi _{\mu }$. fields are introduced explicitly level Lagrangian means standard procedures. consider two options, where quantized as physical particle or fakeon, compute absorptive part self-energy multiplet. width }$, negative, shows that predicts violation causality energies...

A theory of quantum gravity has been recently proposed by means a novel quantization prescription, which is able to turn the poles free propagators that are due higher derivatives into fakeons. The classical Lagrangian contains cosmological term, Hilbert $\sqrt{-g}R_{\mu \nu }R^{\mu }$ and $\sqrt{-g}R^{2}$. In this paper, we compute one-loop renormalization absorptive part graviton self energy. results illustrate mechanism makes renormalizability compatible with unitarity. fakeons...

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, the free field limit and, at bare level, presence of interactions. As n-dimensional generalization (conformal) vector field, (n/2-1)-form is used. The two-point functions and higher-spin central charges evaluated one loop. an application, hierarchies generated by stress-tensor operator-product expansion computed supersymmetric theories. results exhibit interesting universality.

We study the standard-model extensions that have following features: they violate Lorentz invariance explicitly at high energies; are unitary, local, polynomial and renormalizable by weighted power counting; contain vertex $(LH{)}^{2}$, which gives Majorana masses to neutrinos after symmetry breaking, possibly four fermion interactions; do not right-handed neutrinos, nor other extra fields. simplest $CPT$ invariant extension of this type in detail prove cancellation gauge anomalies....

The search for purely virtual quanta has attracted interest in the past. We consider various proposals and compare them to concept of fake particle, or "fakeon". In particular, Feynman-Wheeler propagator, which amounts using Cauchy principal value inside Feynman diagrams, violates renormalizability, unitarity stability, due coexistence prescriptions $\pm i\epsilon $. contrast Feynman, fakeon ordinary as well cut diagrams. does not have problems propagator emerges correct quantum. It allows...

A bstract We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual fakeon prescription). The are derived means algebraic operations hold for every (multi)threshold separately arbitrary frequencies. Their major significance is that they offer a deeper understanding on problem unitarity theory. In particular, apply to “skeleton” diagrams, before integrating space components loop momenta phase spaces. turn,...

We address the problem of constructing family (4,4) theories associated with σ model on a parametrized ℳ ζ asymptotically locally Euclidean (ALE) manifolds. rely ADE classification these manifolds and their construction as hyper-Kähler quotients, due to Kronheimer. By so doing we are able define corresponding ALE deformation solvable orbifold C 2 /Γ conformal field theory, Γ being Kleinian group. discuss relation between algebraic structure underlying topological metric properties self-dual...