Solution to the Ward identities for superamplitudes
Abstract
Supersymmetry and Rsymmetry Ward identities relate onshell amplitudes in a supersymmetric field theory. We solve these Ward identities for N^{ K }MHV amplitudes of the maximally supersymmetric mathcal{N} = 4 and mathcal{N} = 8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and Rinvariant form: it is expressed as a sum of very simple SUSY and {text{SU}}{left( mathcal{N} right)_R} invariant Grassmann polynomials, each multiplied by a “basis amplitude”. For N^{ K }MHV npoint superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU( n  4) corresponding to the rectangular Young diagram with mathcal{N} columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of colorordered singletrace amplitudes in mathcal{N} = 4 gauge theory. We also analyze the more significant reduction that occurs in mathcal{N} = 8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2010
 DOI:
 10.1007/JHEP10(2010)103
 arXiv:
 arXiv:0911.3169
 Bibcode:
 2010JHEP...10..103E
 Keywords:

 Supersymmetric gauge theory;
 Extended Supersymmetry;
 High Energy Physics  Theory
 EPrint:
 29 pages, published version