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تسجيل مستخدم جديدChiral Superstring and CHY Amplitude
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We calculate the chiral string amplitude in pure spinor formalism and take four point amplitude as an example. The method could be easily generalized to $N$ point amplitude by complicated calculations. By doing the usual calculations of string theory first and using a special singular gauge limit, we produce the amplitude with the integral over Dirac $delta$-functions. The Bosonic part of the amplitude matches the CHY amplitude and the Fermionic part gives us the supersymmetric generalization of CHY amplitude. Finally, we also check the dependence on boundary condition for heterotic chiral string amplitudes.
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In cite{Chen:2016fgi} we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles.In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms
of the scattering amplitudes using this differential operator. We introduce a tableau representation for the coefficients appearing in the proposed differential operator. Combining the tableaux with the polynomial forms of the scattering equations, the evaluation of the generalized CHY form becomes a simple combinatoric problem. It is thus possible to obtain the coefficients arising in the differential operator in a straightforward way. We present the procedure for a complete solution of the $n$-gon amplitudes at one-loop level in a generalized CHY form. We also apply our method to fully evaluate the one-loop five-point amplitude in the maximally supersymmetric Yang-Mills theory; the final result is identical to the one obtained by Q-Cut.
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