The N=4 supergravity amplitude

These are the mathematica expressions for the rational parts of the six graviton NMHV one-loop amplitude in N=4 supergravity.

They are accompanying the article ''The N=4 Supergravity NMHV six-point one-loop amplitude'' by David Dunbar and Warren Perkins,
The rational term has three parts
  • Terms arising from standard factorisations R6SF
  • Terms arising from non-standard factorisations R6NF
  • Rational descendants of the integral functions R6RD
  • In total R6= R6SF+ R6NF+ R6RD
    Mathematica files of these are available.
  • R6SF
  • R6NF
  • The rational descendands are arise from one-mass boxes, tho mass boxes and the three mass triangle
    R6RD =R6RD,1m box+ R6RD,2m box+ R6RD,3m tri
  • R6RD,1m box
  • R6RD,2m box
  • The rational descendant of the three-mass triangle R6RD, 3m tri are complicated and the necessary files are given (in gziped tar directories at RD3mtA.tar.gz , RD3mtB.tar.gz , RD3mtC.tar.gz , RD3mtD.tar.gz
    To evaluate and test the rational term a file with some simple macros and instructions is given as as this location . The best option is to download and unzip this directory and then download the four RD3Mt files above into this directory and then to unzip these and read README.txt. This contains the code which verifies the symmetry of R6.

    For completeness we also include the rational coefficients of the bubble integral functions.

    There are two types of coefficient (in a gziped tar directory )
  • The 3:3 Bubbles
  • The 2:4 Bubbles. These have a large Mathematica realisation. These are given as a sum of terms
    Any feedback/corections/suggestions is most welcome Last update 22nd Apr 2016.

    see also the six-gluon amplitude , the seven-gluon amplitude and some gravity amplitudes