G. E. Arutyunov

ON THE ORIGIN OF SUPERGRAVITY BOUNDARY TERMS IN THE ADS/CFT CORRESPONDENCE

The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on the Hamiltonian formulation of the supergravity action, which does not require any boundary terms. Then all the boundary terms of the standard formulation naturally appear by passing from the Hamiltonian version to the Lagrangian one. As examples the graviton part of the supergravity action on the product of

Four graviton scattering amplitude from S**N R**8 supersymmetric orbifold sigma model

AdS_{d+1}

Virasoro amplitude from the S(N) R**24 orbifold sigma model

with a compact Einstein manifold

Elliptic Ruijsenaars–Schneider model from the cotangent bundle over the two-dimensional current group

cal E

Elliptic Ruijsenaars - Schneider model via the Poisson reduction of the affine Heisenberg double

and fermions on

Bicovariant 3D calculus for SLq(2) from Poisson–Lie structures

AdS_{d+1}

On the Hamiltonian structure of the spin Ruijsenaars-Schneider model

are considered. We also discuss conformal transformations of gravity fields on the boundary of

Virasoro amplitude from theS N R24-orbifold sigma model

AdS

R-Matrix quantization of the elliptic Ruijsenaars-Schneider model

and show that they are induced by the isometries of

Graded Poisson Lie structures on classical complex Lie groups

AdS