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Register a new userChiral 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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We consider scattering processes involving N gluonic massless states of open superstrings with certain Regge slope alpha. At the semi-classical level, the string world-sheet sweeps a disk and N gluons are created or annihilated at the boundary. We present exact expressions for the corresponding amplitudes, valid to all orders in alpha, for the so-called maximally helicity violating configurations, with N=4, 5 and N=6. We also obtain the leading O(alpha^2) string corrections to the zero-slope N-gluon Yang-Mills amplitudes.
The six gluon disk amplitude is calculated in superstring theory. This amplitude probes the gauge interactions with six external legs on Dp-branes, in particular including e.g. F^6-terms. The full string S-matrix can be expressed by six generalized multiple hypergeometric functions (triple hypergeometric functions), which in the effective action play an important role in arranging the higher order alpha gauge interaction terms with six external legs (like F^6, D^4 F^4, D^2 F^5, D^6 F^4, D^2 F^6, ...). A systematic and efficient method is found to calculate tree-level string amplitudes by equating seemingly different expressions for one and the same string S-matrix: Comparable to Riemann identities appearing in string-loop calculations, we find an intriguing way of using world-sheet supersymmetry to generate a system of non-trivial equations for string tree-level amplitudes. These equations result in algebraic identities between different multiple hypergeometric functions. Their (six-dimensional) solution gives the ingredients of the string S-matrix. We derive material relevant for any open string six-point scattering process: relations between triple hypergeometric functions, their integral representations and their alpha-(momentum)-expansions given by (generalized) Euler-Zagier sums or (related) Witten zeta-functions.
We study in detail the factorization of the newly obtained two-loop four-particle amplitude in superstring theory. In particular some missing factors from the scalar correlators are obtained correctly, in comparing with a previous study of the factorization in two-loop superstring theory. Some details for the calculation of the factorization of the kinematic factor are also presented.
The full two-loop amplitudes for five massless states in Type~II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The $alpha to 0$ limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type~II supergravity. Investigations of the $alpha$ expansion of the Type~II amplitude and comparisons with predictions from S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.
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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