scholarly journals Genus-zero and genus-one string amplitudes and special multiple zeta values

2020 ◽  
Vol 14 (2) ◽  
pp. 413-452
Author(s):  
Don Zagier ◽  
Federico Zerbini
Keyword(s):  
Multiple Zeta Values ◽  
Genus Zero ◽  
Multiple Zeta ◽  
Zeta Values ◽  
String Amplitudes ◽  
Genus One

scholarly journals Single-Valued Integration and Superstring Amplitudes in Genus Zero

2021 ◽  
Vol 382 (2) ◽  
pp. 815-874
Author(s):  
Francis Brown ◽  
Clément Dupont
Keyword(s):  
Open String ◽  
Closed String ◽  
Laurent Expansion ◽  
Tree Level ◽  
Multiple Zeta Values ◽  
Genus Zero ◽  
Period Map ◽  
Multiple Zeta ◽  
Zeta Values ◽  
String Amplitudes

AbstractWe study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper (Brown and Dupont in Single-valued integration and double copy, 2020). Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp. single-valued multiple zeta values). Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion. This proves the recent conjecture of Stieberger that closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes. Finally, applying a variant of the single-valued formalism for cohomology with coefficients yields the KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.

scholarly journals Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes

2018 ◽  
Vol 51 (28) ◽  
pp. 285401 ◽  
Author(s):  
Johannes Broedel ◽  
Nils Matthes ◽  
Gregor Richter ◽  
Oliver Schlotterer
Keyword(s):  
Open String ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
String Amplitudes

Motivic multiple zeta values relative to μ2

2020 ◽  
Vol 14 (10) ◽  
pp. 2685-2712
Author(s):  
Zhongyu Jin ◽  
Jiangtao Li
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

2015 ◽  
Vol 93 (2) ◽  
pp. 186-193 ◽  
Author(s):  
MASANOBU KANEKO ◽  
MIKA SAKATA
Keyword(s):  
Explicit Formula ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values ◽  
Sum Formula

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

scholarly journals Truncated t-adic symmetric multiple zeta values and double shuffle relations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Masataka Ono ◽  
Shin-ichiro Seki ◽  
Shuji Yamamoto
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals Double tails of multiple zeta values

2017 ◽  
Vol 170 ◽  
pp. 228-249 ◽  
Author(s):  
P. Akhilesh
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals On multiple zeta values and finite multiple zeta values of maximal height

2018 ◽  
Vol 14 (04) ◽  
pp. 975-987
Author(s):  
Hideki Murahara ◽  
Mika Sakata
Keyword(s):  
Explicit Formula ◽  
Alternative Proof ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values

An explicit formula for the height-one multiple zeta values (MZVs) was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values (FMZVs).

scholarly journals Nested Sums of Symbols and Renormalized Multiple Zeta Values

2010 ◽  
Vol 2010 (24) ◽  
pp. 4628-4697 ◽  
Author(s):  
Dominique Manchon ◽  
Sylvie Paycha
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values
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