Effective Gravitational Field of Black Holes

The problem of interpretation of the \hbar^0-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order \hbar^0 to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos correcte

Challenges of D=6 N=(1,1) SYM Theory

Maximally supersymmetric Yang-Mills theories have several remarkable properties, among which are the cancellation of UV divergences, factorization of higher loop corrections and possible integrability. Much attention has been attracted to the N=4 D=4 SYM theory. The N=(1,1) D=6 SYM theory possesses similar properties but is nonrenomalizable and serves as a toy model for supergravity. We consider the on-shell four point scattering amplitude and analyze its perturbative expansion within the spin-helicity and superspace formalism. The integrands of the resulting diagrams coincide with those of the N=4 D=4 SYM and obey the dual conformal invariance. Contrary to 4 dimensions, no IR divergences on mass shell appear. We calculate analytically the leading logarithmic asymptotics in all loops. Their summation leads to a Regge trajectory which is calculated exactly. The leading powers of s are calculated up to six loops. Their summation is performed numerically and leads to a smooth function of s. The leading UV divergences are calculated up to 5 loops. The result suggests the geometrical progression which ends up in a finite expression. This leads us to a radical point of view on nonrenormalizable theories.Comment: 11 pages, 2 figures, Late

Renormalizable 1/N_f Expansion for Field Theories in Extra Dimensions

We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in arbitrary high space-time dimension. First, we consider a simple example of $N$-component scalar filed theory and then extend this approach to Abelian and non-Abelian gauge theories with $N_f$ fermions. In the latter case, due to self-interaction of non-Abelian fields the proposed recipe requires some modification which, however, does not change the main results. The resulting effective coupling is dimensionless and is running in accordance with the usual RG equations. The corresponding beta function is calculated in the leading order and is nonpolynomial in effective coupling. It exhibits either UV asymptotically free or IR free behaviour depending on the dimension of space-time. The original dimensionful coupling plays a role of a mass and is also logarithmically renormalized. We analyze also the analytical properties of a resulting theory and demonstrate that in general it acquires several ghost states with negative and/or complex masses. In the former case, the ghost state can be removed by a proper choice of the coupling. As for the states with complex conjugated masses, their contribution to physical amplitudes cancels so that the theory appears to be unitary.Comment: 32 pages, 20 figure

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

The main aim of this paper is to study the scattering amplitudes in gauge field theories with maximal supersymmetry in dimensions D=6,8 and 10. We perform a systematic study of the leading ultraviolet divergences using the spinor helicity and on-shell momentum superspace framework. In D=6 the first divergences start at 3 loops and we calculate them up to 5 loops, in D=8,10 the first divergences start at 1 loop and we calculate them up to 4 loops. The leading divergences in a given order are the polynomials of Mandelstam variables. To be on the safe side, we check our analytical calculations by numerical ones applying the alpha-representation and the dedicated routines. Then we derive an analog of the RG equations for the leading pole that allows us to get the recursive relations and construct the generating procedure to obtain the polynomials at any order of (perturbation theory) PT. At last, we make an attempt to sum the PT series and derive the differential equation for the infinite sum. This equation possesses a fixed point which might be stable or unstable depending on the kinematics. Some consequences of these fixed points are discussed.Comment: 43 pages, 13 figures, pdf LaTex, v2 minor changes and references adde

Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.Comment: 20 page