Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImplications of nonplanar dual conformal symmetry
122
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Recently, Bern et al observed that a certain class of next-to-planar Feynman integrals possess a bonus symmetry that is closely related to dual conformal symmetry. It corresponds to a projection of the latter along a certain lightlike direction. Previous studies were performed at the level of the loop integrand, and a Ward identity for the integral was formulated. We investigate the implications of the symmetry at the level of the integrated quantities. In particular, we focus on the phenomenologically important case of five-particle scattering. The symmetry simplifies the four-variable problem to a three-variable one. In the context of the recently proposed space of pentagon functions, the symmetry is much stronger. We find that it drastically reduces the allowed function space, leading to a well-known space of three-variable functions. Furthermore, we show how to use the symmetry in the presence of infrared divergences, where one obtains an anomalous Ward identity. We verify that the Ward identity is satisfied by the leading and subleading poles of several nontrivial five-particle integrals. Finally, we present examples of integrals that possess both ordinary and dual conformal symmetry.
rate research
Read More
We show that dual conformal symmetry, mainly studied in planar $mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple observation is that dual conformal transformations preserve unitarity cut conditions for any planar integrals, including those without dual conformal symmetry. Such transformations generate differential equations without raised propagator powers, often with the right hand side of the system proportional to the dimensional regularization parameter $epsilon$. A nontrivial subgroup of dual conformal transformations, which leaves all external momenta invariant, generates integration-by-parts relations without raised propagator powers, reproducing, in a simpler form, previous results from computational algebraic geometry for several examples with up to two loops and five legs. By opening up the two-loop three- and four-point nonplanar diagrams into planar ones, we find a nonplanar analog of dual conformal symmetry. As for the planar case this is used to generate integration-by-parts relations and differential equations. This implies that the symmetry is tied to the analytic properties of the nonplanar sector of the two-loop four-point amplitude of $mathcal N = 4$ super-Yang-Mills theory.
In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest themselves in the famous BDS ansatz conjecture. In hep-th 1611.02179 it was also conjectured that a similar structure of integrals may reappear in d=6. We show that one can systematically, order by order in the number of loops, construct combinations of d=6 integrals with 1/(p^2)^2 propagators with an iterative structure similar to the d=4 case. Such combinations as a whole also respect dual conformal invariance but individual integrals may not.
The S-matrix of a theory often exhibits symmetries which are not manifest from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering amplitudes are imposed by the dual conformal symmetry of planar 4d $mathcal{N}=4$ super Yang-Mills theory and the ABJM theory. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions, which may provide useful insight into the worldvolume theory of M5-branes (if it enjoys such a symmetry). We find that 6d dual conformal symmetry uniquely fixes the integrand of the one-loop 4-point amplitude, and its structure suggests a Lagrangian with more than two derivatives. On integrating out the loop momentum in $6-2 epsilon$ dimensions, the result is very similar to the corresponding amplitude of $mathcal{N}=4$ super Yang-Mills theory. We confirm this result holographically by generalizing the Alday-Maldacena solution for a minimal area string in Anti-de Sitter space to a minimal volume M2-brane ending on pillow-shaped Wilson surface in the boundary whose seams correspond to a null-polygonal Wilson loop. This involves careful treatment of a prefactor which diverges as $1/epsilon$, and we comment on its possible interpretation. We also study 2-loop 4-point integrands with 6d dual conformal symmetry and speculate on the existence of an all-loop formula for the 4-point amplitude.
We find the three-dimensional gravity dual of a process in which two clouds of (1+1)-dimensional conformal matter moving in opposite directions collide. This gives the most general conformally invariant holographic flow in the 1+1 dimensional boundary theory in terms of two arbitrary functions. With a suitable choice of the arbitrary functions the process can be interpreted as an opaque collision of two extended systems with central, fragmentation and interaction regions. Comparison with classical gluon field calculations relates the size of the system with the saturation scale.
A formulation of $mathcal{N} = 2$ supersymmetric Yang-Mills theory with a spacetime-dependent gauge coupling allows to study the breaking of conformal symmetry at the quantum level. The theory has an energy-momentum tensor that is only conserved if an equation of motion for the coupling is imposed. It admits non-trivial solitons, among which the Wu-Yang monopole that can be regularized and turns out to be massless. On the other hand, the ordinary BPS monopole is only a solution in the large $N_c$ limit.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
