A
bstract
Elliptic multiple polylogarithms occur in Feynman integrals and in particular in scattering amplitudes. They can be characterized by their symbol, a tensor product in the so-called symbol ...letters. In contrast to the non-elliptic case, the elliptic letters themselves satisfy highly non-trivial identities, which we discuss in this paper. Moreover, we introduce the symbol prime, an analog of the symbol for elliptic symbol letters, which makes these identities manifest. We demonstrate its use in two explicit examples at two-loop order: the unequal-mass sunrise integral in two dimensions and the ten-point double-box integral in four dimensions. Finally, we also report the result of the polylogarithmic nine-point double-box integral, which arises as the soft limit of the ten-point integral.
A
bstract
We describe how to calculate the Hagedorn temperature of
N
= 4 SYM theory and type IIB superstring theory on
AdS
5
×
S
5
via the Quantum Spectral Curve (QSC) — providing further details on ...our previous letters
1
and
2
. We solve the QSC equations perturbatively at weak ‘t Hooft coupling
λ
up to seven-loop order and numerically at finite coupling, finding that the perturbative results can be expressed in terms of single-valued harmonic polylogarithms. Moreover, we generalize the QSC to describe the Hagedorn temperature in the presence of chemical potentials. Finally, we show that the Hagedorn temperature in certain deformations of
N
= 4 SYM theory (real-
β
and
γ
i
deformation) agrees with the one in
N
= 4 SYM theory at any value of
λ
.
We show that an integrable four-dimensional non-unitary field theory that was recently proposed as a certain limit of the γi-deformed N=4 SYM theory is incomplete and not conformal – not even in the ...planar limit. We complete this theory by double-trace couplings and find conformal one-loop fixed points when admitting respective complex coupling constants. These couplings must not be neglected in the planar limit, as they can contribute to planar multi-point functions. Based on our results for certain two-loop planar anomalous dimensions, we propose tests of integrability.
Building on the recently established connection between the Hagedorn temperature and integrability 1, we show how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn ...temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this finite system of finite-difference equations perturbatively at weak coupling and numerically at finite coupling. We confirm previous results at weak coupling and obtain the previously unknown three-loop Hagedorn temperature. Our finite-coupling results interpolate between weak and strong coupling and allow us to extract the first perturbative order at strong coupling. Our results indicate that the Hagedorn temperature for large 't Hooft coupling approaches that of type IIB string theory in ten-dimensional Minkowski space.
A
bstract
It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large ...dimension. While the number of Calabi-Yau manifolds of dimension three or higher is considerable (if not infinite), those relevant to most known examples come from a very simple class: degree-2
k
hypersurfaces in
k
-dimensional weighted projective space WP
1
,...,
1
,k
. In this work, we describe some of the basic properties of these spaces and identify additional examples of Feynman integrals that give rise to hypersurfaces of this type. Details of these examples at three loops and of illustrations of open questions at four loops are included as supplementary material to this work.
A three-point form factor through five loops Dixon, Lance J.; McLeod, Andrew J.; Wilhelm, Matthias
The journal of high energy physics,
04/2021, Letnik:
2021, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A
bstract
We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar
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
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
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.
A
bstract
Form factors in planar
N
= 4 Super-Yang-Mills theory admit a type of non-perturbative 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 supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.
A quantum check of non-supersymmetric AdS/dCFT Grau, Aleix Gimenez; Kristjansen, Charlotte; Volk, Matthias ...
The journal of high energy physics,
01/2019, Letnik:
2019, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A
bstract
Via a challenging field-theory computation, we confirm a supergravity prediction for the non-supersymmetric D3-D7 probe-brane system with probe geometry
AdS
4
×
S
2
×
S
2
, stabilized by ...fluxes. Supergravity predicts, in a certain double-scaling limit, the value of the one-point functions of chiral primaries of the dual defect version of
N
=
4
SYM theory, where the fluxes translate into SO(3) × SO(3)-symmetric, Lie-algebra-valued vacuum expectation values for all six scalar fields. Using a generalization of the technique based on fuzzy spherical harmonics developed for the related D3-D5 probe-brane system, we diagonalize the resulting mass matrix of the field theory. Subsequently, we calculate the planar one-loop correction to the vacuum expectation values of the scalars in dimensional reduction and find that it is UV finite and non-vanishing. We then proceed to calculating the one-loop correction to the planar one-point function of any single-trace scalar operator and explicitly evaluate this correction for a 1/2-BPS operator of length
L
at two leading orders in the double-scaling limit, finding exact agreement with the supergravity prediction.
Rationalizing loop integration Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt ...
The journal of high energy physics,
08/2018, Letnik:
2018, Številka:
8
Journal Article
Recenzirano
Odprti dostop
A
bstract
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal ...Feynman-parametric representations of planar loop integrals, and the fact that many of the algebraic roots associated with (e.g. Landau) leading singularities are automatically rationalized in momentum-twistor space — facilitating direct integration via partial fractioning. We describe how momentum twistors may be chosen non-redundantly to parameterize particular integrals, and how strategic choices of coordinates can be used to expose kinematic limits of interest. We illustrate the power of these ideas with many concrete cases studied through four loops and involving as many as eight particles. Detailed examples are included as supplementary material.
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