Abstract
We consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum $q^2=0$. We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts. The presented conjecture was successfully checked by reproducing several known answers in $\mbox{MHV}$ and $\mbox{N}^{k-2}\mbox{MHV}$, $k\geq3$ sectors together with appropriate soft limits. We also discuss the cancellation of spurious poles and relations between different BCFW representations for such form factors on simple examples.
Highlights
There is another class of interesting objects in N = 4 SYM similar to amplitudes-form factors
We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts
One may wonder whether it is possible to construct a representation for form factors which will be given by a single term and be manifestly cyclically invariant? it is interesting to find an analogs of the objects considered here within context of twistor string theories
Summary
We would like to discuss how the cancellation of spurious poles and the relations between different BCFW representations for form factors follow from our Grassmannian representation. It is tempting to try to reproduce analytical expression for [2, 3 BCFW shift representation of NMHV5 form factor as the sum over residues given by contour (see figure 13) Γ246∗.12. The careful reader may already noticed that the discussion of the relations between different BCFW representations is somewhat redundant (at least in the NMHV case), because momentum conservation in this case allows one to rewrite the set of poles P [1,2 in a manifestly cyclically invariant form. We expect that similar situation will occur in more complicated cases with Nk−2MHV form factors in full analogy with the amplitude case This brings us to the following questions: is it possible to interpret the residues of (4.1) as a basis for the leading singularities of form factors and whether there is a general prescription for the choice of integration contour in more complicated cases of Nk−2MHV form factors? We may conjecture that in the general case the integration contour appropriate for the Nk−2MHVn form factors may be chosen similar to the case of Nk−2MHVn+1 amplitude ([1, 2 BCFW representation)
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