Related papers: Getting superstring amplitudes by degenerating Rie…
We show that the higher genus 4-point superstring amplitude is strongly constrained by the geometry of moduli space of Riemann surfaces. A detailed analysis leads to a natural proposal which satisfies several conditions. The result is based…
In this paper we continue the program pioneered by D'Hoker and Phong, and recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the chiral superstring measure by constructing modular forms satisfying certain…
The relation between superholomorphicity and holomorphicity of chiral superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is shown to be encoded in a hybrid cohomology theory, incorporating elements of both de Rham and…
Very recently, Grushevsky continued D'Hoker and Phong's program of finding the chiral superstring measure from first principles by constructing modular forms satisfying certain factorization constraints. He has proposed an ansatz in genus 4…
A systematic construction of superstring scattering amplitudes for $N$ massless NS bosons to two loop order is given, based on the projection of supermoduli space onto super period matrices used earlier for the superstring measure in the…
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…
The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help…
By replacing two of the bosonic scalar superfields of the N=2 string with fermionic scalar superfields (which shifts $d_{critical}$ from (2,2) to (9,1)), a quadratic action for the ten-dimensional Green-Schwarz superstring is obtained.…
We show that a recently conjectured expression for the superstring three-point amplitude, in the framework of the Cacciatori, Dalla Piazza, van Geemen - Grushevsky ansatz for the chiral measure, fails to vanish at three-loop, in contrast…
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…
We generalize the super period matrix of a super Riemann surface to the case that Ramond punctures are present. For a super Riemann surface of genus g with 2r Ramond punctures, we define, modulo certain choices that generalize those in the…
Closed string amplitudes at genus $h\leq 3$ are given by integrals of Siegel modular functions on a fundamental domain of the Siegel upper half-plane. When the integrand is of rapid decay near the cusps, the integral can be computed by the…
The N-point amplitudes for the Type II and Heterotic superstrings at two-loop order and for $N \leq 4$ massless NS bosons are evaluated explicitly from first principles, using the method of projection onto super period matrices introduced…
In this paper, we proposed a worldsheet construction of a subset of triple product amplitudes proposed by Huang and Remmen (2022). We start with closed bosonic strings but left and right-moving momenta are not necessarily equal. Instead,…
In a very recent preprint, Witten showed how to construct a $g|r \, \times \, g|r$ super period matrix for super Riemann surfaces of genus $g$ with $2r$ Ramond punctures, which is symmetric in the ${\bf Z}_2$ graded sense. He also showed…
We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space…
The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this…
We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is…
The two-loop chiral measure for superstring theories compactified on $\bZ_2$ reflection orbifolds is constructed from first principles for even spin structures. This is achieved by a careful implementation of the chiral splitting procedure…
In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless particles, and for expressing them in manifestly Lorentz-invariant form. By…