1,592 research outputs found
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
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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
-expansion and results in a logarithmically divergent perturbation
theory in arbitrary high space-time dimension. First, we consider a simple
example of -component scalar filed theory and then extend this approach to
Abelian and non-Abelian gauge theories with 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
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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
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