Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure

By Carlos R. Mafra, O. Schlotterer, S. Stieberger. 2011

228 citations recorded by the source corpus.

Using the pure spinor formalism in part I (Mafra et al., preprint [1]) we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed by a sum over (N − 3)! Yang–Mills partial subamplitudes each multiplying a multiple Gaussian hypergeometric function. While the former capture the space–time kinematics of the amplitude the latter encode the string effects. This result disguises a lot of structure linking aspects of gauge amplitudes as color and kinematics with properties of generalized Euler integrals. In this part II the structure of the multiple hypergeometric functions is analyzed in detail: their relations to monodromy equations, their minimal basis structure, and methods to determine their poles and transcendentality properties are proposed. Finally, a Grobner basis analysis provides independent sets of rational functions in the Euler integrals. © 2013 Elsevier B.V. All rights reserved.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dde70dda4c619de81de0a01e99a29894a68c8600

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. C. Cheung
2. F. Cachazo
3. Song He
4. L. Mason
5. Tim Adamo
6. N. Arkani-Hamed
7. S. Stieberger
8. E. Y. Yuan

In Statistical and Nonlinear Physics

1. F. Cachazo
2. Song He
3. S. Stieberger
4. L. Mason
5. E. Y. Yuan
6. C. Cheung
7. R. Monteiro
8. O. Schlotterer

Citations in the corpus

• Closed string amplitudes as single-valued open string amplitudes (2014, background): “2) can be given by the matrix expression A = FA [19,20].”
• Polylogarithms, multiple zeta values and superstring amplitudes (2013, methodology): “5 of [7] accordingly follows by the action of σ ∈ SN−2 on ∑ ρ∈SN−3 S[2, .”
• Scattering equations and Kawai-Lewellen-Tye orthogonality (2013, background): “Recently [19, 20] it was shown that superstring disk amplitudes can be expressed as linear combinations of (n−3)! Yang-Mills partial amplitudes (e.”
• Pure gravities via color-kinematics duality for fundamental matter (2014, unknown): “n2 = 〈13〉 ( [24] 〈q|2|5] 〈q5〉 + [25][54] ) , (2.”
• Scattering forms and the positive geometry of kinematics, color and the worldsheet (2017, background): “[34]), there must be deep conceptual reasons why the gauge-invariant object for gluon scattering in YM theory completely dictates the infinite series of higherdimensional corrections from superstrings! It would be highly desirable to understand this fact better and to see in general how integrals an”
• Unifying relations for scattering amplitudes (2017, background): “By transmuting two pairs of gluons, we obtain the scattering amplitudes for biadjoint scalars, A(φ1φ2, φ3φ4) = T [12] · T [34] · A(g1, g2, g3, g4) = p1p3 p1p2 A(φ1φ3, φ2φ4) = T [13] · T [24] · A(g1, g2, g3, g4) = 1 .”
• Complete N-point superstring disk amplitude I. Pure spinor computation (2011, methodology): “by an equal number of hypergeometric integrals, as mentioned in the Introduction and further elaborated in [2].”
• Ambitwistor strings and the scattering equations at one loop (2013, methodology): “J H E P 0 4 ( 2 0 1 4 ) 1 0 4 correlators in these pure spinor models in closed form, perhaps using the methods of [18].”
• Scattering of massless particles: scalars, gluons and gravitons (2013, methodology): “The inverse of the KLT matrix has also been discussed in [13] where it was related to the field-theory limit of string disk integrals,5 following computations in [14, 15].”
• PolyLogTools — polylogs for the masses (2019, background): “J H E P 0 8 ( 2 0 1 9 ) 1 3 5 We see that indeed all the first entries are proportional to π2, and we can immediately read of the values of the coefficients of the terms in the ansatz proportional to π2: In[13]:= sol2 = {c[17] -> 0, c[18] -> 1/12, c[19] -> 0, c[20] -> 0};”
• Motivic multiple zeta values and superstring amplitudes (2012, methodology): “At string tree–level the complete open string N–point superstring amplitude has been computed in [22,23].”
• Einstein-Yang-Mills scattering amplitudes from scattering equations (2014, methodology): “A concrete possibility is the combination of the work by Mafra, Schlotterer and Stieberger [36, 37], and Berkovits’ infinite tension limit model [20].”
• One-loop amplitudes on the Riemann sphere (2015, methodology): “The n-point amplitude is known, however [56]; using the procedure of [57] it is possible to cherry-pick the 2-fermion-n-boson component of the string amplitude (using [58] for instance).”