scholarly journals Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge kinematics

2017 ◽  
Vol 915 ◽  
pp. 394-413 ◽  
Author(s):  
Johannes Broedel ◽  
Martin Sprenger ◽  
Alejandro Torres Orjuela
Keyword(s):  
Remainder Function

scholarly journals Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Guanda Lin ◽  
Gang Yang
Keyword(s):  
Form Factors ◽  
General Strategy ◽  
Dual Representation ◽  
Remainder Function ◽  
Full Color ◽  
Minimal Form ◽  
Planar Part ◽  
Dilatation Operator ◽  
Dependent Form ◽  
Local Operators

Abstract Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in the SU(2) sector in $$ \mathcal{N} $$ N = 4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors of high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor result provides an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergences, we also reproduce the known non-planar SU(2) dilatation operator at two loops. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.

Test for Divisibility by the Use of a Remainder Function

1958 ◽  
Vol 31 (3) ◽  
pp. 137
Author(s):  
N. A. Draim
Keyword(s):  
Remainder Function

scholarly journals The three-loop MHV octagon from $$ \overline{Q} $$ equations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Zhenjie Li ◽  
Chi Zhang
Keyword(s):  
Yang Mills ◽  
Remainder Function ◽  
Point Amplitude

Abstract The $$ \overline{Q} $$ Q ¯ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. By using the $$ \overline{Q} $$ Q ¯ equations, we compute the symbol of the first MHV amplitude with algebraic letters — the three-loop 8-point amplitude (or the octagon remainder function) — in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

Is the Euclidean Algorithm Optimal Among its Peers?

2004 ◽  
Vol 10 (3) ◽  
pp. 390-418 ◽  
Author(s):  
Lou Van Den Dries ◽  
Yiannis N. Moschovakis
Keyword(s):  
Natural Number ◽  
Rational Number ◽  
Time Complexity ◽  
Euclidean Algorithm ◽  
Worst Case ◽  
On Demand ◽  
Recursive Program ◽  
Remainder Function ◽  
Proper Formulation ◽  
Image Position

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem(a, b) is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from (relative to) the remainder function rem, meaning that in computing its time complexity function cε (a, b), we assume that the values rem(x, y) are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch more is known about cε(a, b), but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's (worst case) optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd (x,y) from rem with time complexity cα (x,y), then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα (a,b) > r log2a.

scholarly journals Exploring Reggeon bound states in strongly-coupled $$ \mathcal{N} $$ = 4 super Yang-Mills

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Theresa Abl ◽  
Martin Sprenger
Keyword(s):  
Analytic Continuation ◽  
Bound States ◽  
Large Mass ◽  
Bound State ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Remainder Function ◽  
Regge Limit ◽  
Case Basis ◽  
Number Of Particles

Abstract The multi-Regge limit of scattering amplitudes in strongly-coupled $$ \mathcal{N} $$ N = 4 super Yang-Mills is described by the large mass limit of a set of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function arises in this setup in certain kinematical regions due to excitations of the TBA equations which appear during the analytic continuation into these kinematical regions. So far, these analytic continuations were carried out on a case-by-case basis for the six- and seven-gluon remainder function. In this note, we show that the set of possible excitations appearing in any analytic continuation in the multi-Regge limit for any number of particles is rather constrained. In particular, we show that the BFKL eigenvalue of any possible Reggeon bound state is a multiple of the two-Reggeon BFKL eigenvalue appearing in the six-gluon case.

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