Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGrassmannians and form factors with $q^2=0$ in N=4 SYM theory
132
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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 $mbox{N}^{k-2}mbox{MHV}$, $kgeq3$ 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.
rate research
Read More
In this paper we study the form factors for the half-BPS operators $mathcal{O}^{(n)}_I$ and the $mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $mathcal{K}$ at first order of perturbation theory in $mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.
Soft theorems for the form factors of 1/2-BPS and Konishi operator supermultiplets are derived at tree level in N=4 SYM theory. They have a form identical to the one in the amplitude case. For MHV sectors of stress tensor and Konishi supermultiplets loop corrections to soft theorems are considered at one loop level. They also appear to have universal form in soft limit. Possible generalization of the on-shell diagrams to the form factors based on leading soft behavior is suggested. Finally, we give some comments on inverse soft limit and integrability of form factors in the limit $q^2to 0$
We construct the most general composite operators of N = 4 SYM in Lorentz harmonic chiral ($approx$ twistor) superspace. The operators are built from the SYM supercurvature which is nonpolynomial in the chiral gauge prepotentials. We reconstruct the full nonchiral dependence of the supercurvature. We compute all tree-level MHV form factors via the LSZ redcution procedure with on-shell states made of the same supercurvature.
In this paper we develop a supersymmetric version of unitarity cut method for form factors of operators from the chiral truncation of the the $mathcal{N}=4$ stress-tensor current supermultiplet $T^{AB}$. The relation between the superform factor with supermomentum equals to zero and the logarithmic derivative of the superamplitude with respect to the coupling constant is discussed and verified at tree- and one-loop level for any MHV $n$-point ($n geq 4$) superform factor involving operators from chiral truncation of the stress-tensor energy supermultiplet. The explicit $mathcal{N}=4$ covariant expressions for n-point tree- and one-loop MHV form factors are obtained. As well, the ansatz for the two-loop three-point MHV superform 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 tree- and one-loop level are discussed.
In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $mathcal{N}=4$ SYM. For the off-shell amplitudes with one leg off-shell we present a conjecture for their Grassmannian integral representation in spinor helicity, twistor and momentum twistor parameterizations. The presented conjecture is successfully checked against BCFW results for MHV$_n$, NMHV$_4$ and NMHV$_5$ off-shell amplitudes. We have also verified that our Grassmannian integral representation correctly reproduces soft (on-shell) limit for the off-shell gluon momentum. It is shown that the (deformed) off-shell amplitude expressions could be also obtained using quantum inverse scattering method for auxiliary $gl(4|4)$ super spin chain.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
