676 research outputs found
On a Large N Degeneracy in N=4 SYM and the AdS/CFT Correspondence
We study the four-point correlator of 1/2-BPS operators of weight 4 in N=4
SYM, which are dual to massive KK modes in AdS_5 supergravity. General
field-theoretic arguments lead to a partially non-renormalized form of the
amplitude that depends on two a priori independent functions of the conformal
cross-ratios. We explicitly compute the amplitude in the large N limit at one
loop (order g^2) and in AdS_5 supergravity. Surprisingly, the one-loop result
shows that the two functions determining the amplitude coincide while in the
supergravity regime they are distinctly different. We discuss the possible
implications of this perturbative degeneracy for the AdS/CFT correspondence.Comment: 32 pages, 5 figures, LaTex, the Summary and Conclusions section
extended, references adde
Four-point correlators of BPS operators in N=4 SYM at order g^4
We study the large N degeneracy in the structure of the four-point amplitudes
of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At
one loop (order g^2) this degeneracy manifests itself in a smaller number of
independent conformal invariant functions describing the amplitude, compared to
AdS_5 supergravity results. To study this phenomenon at the two-loop level
(order g^4) we consider a particular N=2 hypermultiplet projection of the
general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then
explicitly compute this four-point correlator at two loops and identify the
corresponding conformal invariant functions. In the cases of 1/2-BPS operators
of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop
corrections. However, for weight k > 4 the degeneracy is still there at the
two-loop level. This behavior suggests that for a given weight k the degeneracy
will be removed if perturbative corrections of sufficiently high order are
taken into account. These results are in accord with the AdS/CFT duality
conjecture.Comment: 45 pages, latex, 14 figure
On Hamiltonian structure of the spin Ruijsenaars-Schneider model
The Hamiltonian structure of spin generalization of the rational
Ruijsenaars-Schneider model is found by using the Hamiltonian reduction
technique. It is shown that the model possesses the current algebra symmetry.
The possibility of generalizing the found Poisson structure to the
trigonometric case is discussed and degeneration to the Euler-Calogero-Moser
system is examined.Comment: latex, 16 pages, references are adde
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