On MHV form factors in superspace for $ \mathcal{N} = 4 $ SYM theory

Abstract

In this paper we develop a supersymmetric version of a unitarity cut method for form factors of operators from the N = 4 stress-tensor current supermultiplet T AB . The relation between the super form factor with super momentum equal to zero and the logarithmic derivative of the superamplitude with respect to the coupling constant is discussed and verified at the tree-and one-loop level for any MHV n-point (n ≥ 4) super form factor. The explicit N = 4 covariant expressions for n-point MHV tree-and one-loop form factors are obtained. As well, the ansatz for the two-loop three-point MHV super form factor is suggested in the planar limit, based on the reduction procedure for the scalar integrals suggested in our previous work. The different soft and collinear limits in the MHV sector at the tree-and one-loop level are discussed.

Lagrangian insertion in the light-like limit and the super-correlators/super-amplitudes duality

“…Generalized unitarity can also be applied to objects containing local gauge-invariant operators such as correlation functions [5] and form factors [6,7,[26][27][28][29][30][31][32][33][34][35][36]. Since generalized unitarity is a momentum space method, the local operators will have to be Fourier transformed.…”

On soft theorems and form factors in N = 4 $$ \mathcal{N}=4 $$ SYM theory

“…Taking into account that F p,n is chiral and translationally invariant, while T p is 1/2-BPS and considering the corresponding Ward identities, we see that the form factor F p,n should satisfy the following set of conditions [29]:…”

“…It is also interesting to note that in the limit when (super)momentum carried by operator goes to zero (q, γ) → 0 form factors have different, but still universal and well defined behavior (see [29]):…”

Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory

“…After nearly a decade the investigation of 1/2-BPS form factors was again initiated in [32,33]. Later the form factors of operators from 1/2-BPS and Konishi operator supermultiplets were intensively investigated both at weak [34][35][36][37] and strong couplings [38,39]. Attempts to find a geometrical interpretation of form factors of operators from stress tensor operator supermultiplet were performed in [40].…”

“…At the same time, while the behavior of form factor when one of the momenta associated with external particles become soft is essentially identical to the amplitude case, its behavior in the limit when the momentum of the operator q becomes soft (q and its Grassmann counterpart γ (q, γ) → 0) is different. In fact, the following relation holds 8 (see [35]):…”