[SLAC] [SLAC Pubs and Reports] SLAC-PUB-7751On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences 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 $D$-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. (Equations render on Windows, Mac OS, AIX, Linux, Solaris, and IRIX with the techexplorer plug-in.) Full Text PDF slac-pub-7751 (3.85 MB) Compressed PostScript slac-pub-7751 (375 KB) Alternate download methods: old, ancient* *download methods - technical info techexplorer slac-pub-7751 (8.93 KB) More Information Full bibliographic data for this document, including its complete author list, is (or soon will be) available from SLAC's SPIRES-HEP Database. Please report problems with this file to posting@slac.stanford.edu. The SLAC preprint inventory is provided by the SLAC Technical Publications Department. Page generated 04 Apr 2001 @ 15:08 PDT by htmlme.pl
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. (Equations render on Windows, Mac OS, AIX, Linux, Solaris, and IRIX with the techexplorer plug-in.)
(Equations render on Windows, Mac OS, AIX, Linux, Solaris, and IRIX with the techexplorer plug-in.)
PDF slac-pub-7751 (3.85 MB) Compressed PostScript slac-pub-7751 (375 KB) Alternate download methods: old, ancient* *download methods - technical info techexplorer slac-pub-7751 (8.93 KB)
Full bibliographic data for this document, including its complete author list, is (or soon will be) available from SLAC's SPIRES-HEP Database.