Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new user6d Dual Conformal Symmetry and Minimal Volumes in AdS
130
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
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.
Field theories in black hole spacetimes undergo dimensional reduction near horizon (in the Rindler limit) to two dimensional conformal field theories. We investigate this enhancement of symmetries in the context of gauge/gravity duality by considering Rindler space as boundary of Anti-de Sitter space in three spacetime dimensions. We show that the loxodromy conjugacy class of the SO(2,2) isometry group is responsible for generating the special conformal transformations on the boundary under RG flow. We use this approach to present an alternative derivation of the two-point function in Rindler space using AdS/CFT correspondence.
A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose non-primary character conspires with the non-invariance of the vacuum to give precisely the correlation functions in a conformally invariant theory.
We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D $mathcal{N}=4$ SYM and extends the previous construction of the enhanced dual conformal algebra for 6D $mathcal{N}=(1,1)$ SYM to the full 6D dual superconformal algebra for chiral theories. We formulate constraints in 6D spinor helicity formalism and find all generators of the 6D dual superconformal algebra. Next we check that they agree with the dual superconformal generators of known 3D and 4D theories. We show that it is possible to significantly simplify the form of generators and compactly write the dual superconformal algebra using superindices. Finally, we work out some examples of algebra invariants.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
