Triangle Seminars
Wednesday, 18 Jan 2017
Space-time CFTs from the Riemann sphere
📍 London
Tim Adamo
(Imperial College)
Abstract:
In recent years, there has been significant process in the study of perturbative field theory scattering amplitudes using certain 2d chiral, first-order CFTs known as 'ambitwistor string theories.' After a brief review of the ambitwistor setup, I will introduce a related family of 2d CFTs, which can be viewed as constrained ambitwistor strings. These new models describe holomorphic maps from the Riemann sphere to the projective null cone in D-dimensional Minkowski space. This target space is the natural setting to describe field theories with (classical) conformal invariance in (D-2)-dimensions. Killing the anomalies associated with these models fixes critical dimensions for which three well-known space-time field theories (bi-adjoint cubic scalar, gauge theory, gravity) are conformal. Furthermore, the spectrum of each model contains all single field insertions, along with their conformal descendants, of the correct scaling dimension. Time permitting, I will also outline how the space-time 3-point functions can be obtained from the 3-point correlators on the Riemann sphere.
In recent years, there has been significant process in the study of perturbative field theory scattering amplitudes using certain 2d chiral, first-order CFTs known as 'ambitwistor string theories.' After a brief review of the ambitwistor setup, I will introduce a related family of 2d CFTs, which can be viewed as constrained ambitwistor strings. These new models describe holomorphic maps from the Riemann sphere to the projective null cone in D-dimensional Minkowski space. This target space is the natural setting to describe field theories with (classical) conformal invariance in (D-2)-dimensions. Killing the anomalies associated with these models fixes critical dimensions for which three well-known space-time field theories (bi-adjoint cubic scalar, gauge theory, gravity) are conformal. Furthermore, the spectrum of each model contains all single field insertions, along with their conformal descendants, of the correct scaling dimension. Time permitting, I will also outline how the space-time 3-point functions can be obtained from the 3-point correlators on the Riemann sphere.
Posted by: KCL
Holographic Entanglement Entropy for the Gravitational Anomaly in Four Dimensions
Jeff Murugan
(Cape Town U.)
Abstract:
We compute the holographic entanglement entropy for the pure gravitational anomaly in 3+1 dimensions. Using the perturbative method developed for com- puting entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contribu- tions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.
We compute the holographic entanglement entropy for the pure gravitational anomaly in 3+1 dimensions. Using the perturbative method developed for com- puting entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contribu- tions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.
Posted by: QMW
Thursday, 19 Jan 2017
6d Dual Conformal Symmetry and Minimal Volumes in AdS
Arthur Lipstein
(Durham)
Abstract:
The planar scattering amplitudes of 4d N = 4 super Yang-Mills theory and 3d N=6 Chern-Simons theory exhibit a remarkable property known as dual conformal symmetry. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions. We find that 6d dual conformal symmetry fixes the structure of the one-loop 4-point amplitude and suggests a Lagrangian with more than two derivatives. Moreover, we obtain a similar structure by generalizing the Alday-Maldacena solution for a string in Anti-de Sitter space to a 2-brane ending on a pillow-shaped surface in the boundary whose seams correspond to a null-polygon, which suggests an all-loop formula for the 4-point amplitude similar to that of N=4 super Yang-Mills theory.
The planar scattering amplitudes of 4d N = 4 super Yang-Mills theory and 3d N=6 Chern-Simons theory exhibit a remarkable property known as dual conformal symmetry. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions. We find that 6d dual conformal symmetry fixes the structure of the one-loop 4-point amplitude and suggests a Lagrangian with more than two derivatives. Moreover, we obtain a similar structure by generalizing the Alday-Maldacena solution for a string in Anti-de Sitter space to a 2-brane ending on a pillow-shaped surface in the boundary whose seams correspond to a null-polygon, which suggests an all-loop formula for the 4-point amplitude similar to that of N=4 super Yang-Mills theory.
Posted by: IC