Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-02-23
Nucl.Phys.B530:401-456,1998
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 52 pages, discussion of 2 loop divergences in D=8,10 added
Scientific paper
10.1016/S0550-3213(98)00420-9
String theory implies that field theories containing gravity are in a certain sense `products' of gauge theories. We make this product structure explicit up to two loops for the relatively simple case of N=8 supergravity four-point amplitudes, demonstrating that they are `squares' of N=4 super-Yang-Mills amplitudes. This is accomplished by obtaining an explicit expression for the $D$-dimensional two-loop contribution to the four-particle S-matrix for N=8 supergravity, which we compare to the corresponding N=4 Yang-Mills result. From these expressions we also obtain the two-loop ultraviolet divergences in dimensions D=7 through D=11. The analysis relies on the unitarity cuts of the two theories, many of which can be recycled from a one-loop computation. The two-particle cuts, which may be iterated to all loop orders, suggest that squaring relations between the two theories exist at any loop order. The loop-momentum power-counting implied by our two-particle cut analysis indicates that in four dimensions the first four-point divergence in N=8 supergravity should appear at five loops, contrary to the earlier expectation, based on superspace arguments, of a three-loop counterterm.
Bern Zvi
Dixon Lance
Dunbar David C.
Perelstein Maxim
Rozowsky Joel S.
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