On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences
Feb, 1998
51 pages
Published in:
- Nucl.Phys.B 530 (1998) 401-456
e-Print:
- hep-th/9802162 [hep-th]
Report number:
- SLAC-PUB-7751,
- UCLA-98-TEP-03,
- SWAT-98-183
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Abstract:
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 -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.Note:
- Latex, 52 pages, discussion of 2 loop divergences in D=8,10 added Report-no: SLAC-PUB-7751, UCLA/98/TEP/03, SWAT-98-183
- 04.50.+h
- 04.65.+e
- 04.60.-m
- Unitarity
- Cutting
- Ultraviolet divergences
- Supersymmetry
- Supergravity
- Two-loops
- Multi-loops
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