Abstract:Form factors in planar N = 4 Super-Yang-Mills theory admit a type of nonperturbative operator product expansion (OPE), as we have recently shown in [1]. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supe… Show more
“…6 6. Near-collinear limit: The near collinear limit of R should agree with the predictions of the FFOPE [60][61][62].…”
Section: Discontinuitymentioning
confidence: 74%
“…Their expansion around this limit is described at all loop orders by the integrability-based pentagon operator product expansion (POPE) [50][51][52][53][54][55][56][57][58][59]. Recently, an analogous description of the near-collinear limit of form factors has been developed, termed the form factor operator product expansion (FFOPE) [60][61][62]. It provides physical constraints on the near-collinear behavior of the form factors of the chiral part of the stress-tensor supermultiplet at any loop order.…”
Section: Jhep04(2021)147mentioning
confidence: 99%
“…An important source of data for the perturbative form factor bootstrap stems from the near-collinear limit. Using the recently developed form factor operator product expansion, or FFOPE, the form factor can be determined in an expansion around the collinear limit for any value of the planar coupling constant [60][61][62]. Let us briefly review this construction.…”
Section: Near-collinear Limit Via Integrabilitymentioning
confidence: 99%
“…Note that dual conformal symmetry acts on both the dual momenta and the periodicity constraint. Using dual momentum space, the expectation value of the (suitably regularized) Wilson loop can be written in terms of dual conformal cross ratios [60]. For the three-point form factor, we have…”
Section: Near-collinear Limit Via Integrabilitymentioning
We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar $$ \mathcal{N} $$
N
= 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ* → $$ q\overline{q}g $$
q
q
¯
g
. We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $$ \mathcal{N} $$
N
= 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.
“…6 6. Near-collinear limit: The near collinear limit of R should agree with the predictions of the FFOPE [60][61][62].…”
Section: Discontinuitymentioning
confidence: 74%
“…Their expansion around this limit is described at all loop orders by the integrability-based pentagon operator product expansion (POPE) [50][51][52][53][54][55][56][57][58][59]. Recently, an analogous description of the near-collinear limit of form factors has been developed, termed the form factor operator product expansion (FFOPE) [60][61][62]. It provides physical constraints on the near-collinear behavior of the form factors of the chiral part of the stress-tensor supermultiplet at any loop order.…”
Section: Jhep04(2021)147mentioning
confidence: 99%
“…An important source of data for the perturbative form factor bootstrap stems from the near-collinear limit. Using the recently developed form factor operator product expansion, or FFOPE, the form factor can be determined in an expansion around the collinear limit for any value of the planar coupling constant [60][61][62]. Let us briefly review this construction.…”
Section: Near-collinear Limit Via Integrabilitymentioning
confidence: 99%
“…Note that dual conformal symmetry acts on both the dual momenta and the periodicity constraint. Using dual momentum space, the expectation value of the (suitably regularized) Wilson loop can be written in terms of dual conformal cross ratios [60]. For the three-point form factor, we have…”
Section: Near-collinear Limit Via Integrabilitymentioning
We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar $$ \mathcal{N} $$
N
= 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, “extended-Steinmann-like” conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. At two loops, the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ* → $$ q\overline{q}g $$
q
q
¯
g
. We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $$ \mathcal{N} $$
N
= 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.
“…Another important structure to explore is the color-kinematics duality, in particular for form factors of general non-BPS operators at two loops. Furthermore, the form factors at strong coupling via AdS/CFT have been studied in [4,5,12], and more recently, the Pentagon OPE method has been generalized to form factor [136]. It would be certainly interesting to have a non-planar generalization (see a related study for amplitudes [137]).…”
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.
We present the Sudakov form factor in full color $$ \mathcal{N} $$
N
= 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.
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