Triangle Seminars
Tuesday, 22 Jan 2019
Graphene and Boundary Conformal Field Theory
Chris Herzog
(King's)
Abstract:
The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling – the charge of the electron – which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.
The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling – the charge of the electron – which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.
Posted by: CityU2
Wednesday, 23 Jan 2019
What spatial geometry does the (2+1)-d QFT vacuum prefer?
📍 London
Toby Wiseman
(Imperial College London)
Abstract:
We consider the energy of a (2+1)-d relativistic QFT on a
deformation of flat space in either the quantum or thermal vacuum state.
Looking at both free scalars and fermions, with and without mass (and in
the scalar case including a curvature coupling) we surprisingly find
that any deformation of flat space is always energetically preferred to
flat space itself. This is a UV finite effect, insensitive to any cut-
off. We see the same behaviour for any (2+1)-holographic CFT which we
compute via the gravity dual. We consider the physical application of this to membranes carrying
relativistic degrees of freedom, the vacuum energy of which then induce
a tendency for the membrane to crumple. An interesting case is monolayer
graphene, which experimentally is observed to ripple, and on large
scales can be understood as a membrane carrying free massless Dirac degrees
of freedom.
We consider the energy of a (2+1)-d relativistic QFT on a
deformation of flat space in either the quantum or thermal vacuum state.
Looking at both free scalars and fermions, with and without mass (and in
the scalar case including a curvature coupling) we surprisingly find
that any deformation of flat space is always energetically preferred to
flat space itself. This is a UV finite effect, insensitive to any cut-
off. We see the same behaviour for any (2+1)-holographic CFT which we
compute via the gravity dual. We consider the physical application of this to membranes carrying
relativistic degrees of freedom, the vacuum energy of which then induce
a tendency for the membrane to crumple. An interesting case is monolayer
graphene, which experimentally is observed to ripple, and on large
scales can be understood as a membrane carrying free massless Dirac degrees
of freedom.
Posted by: KCL
Thursday, 24 Jan 2019
The Uses of Lattice Topological Defects
Paul Fendley
(Oxford)
Abstract:
I give an overview of work with Aasen and Mong on topological defects in two-dimensional classical lattice models, quantum spin chains and tensor networks. The partition function in the presence of a topological defect is invariant under any local deformation of the defect. By using results from fusion categories, we construct topological defects in a wide class of lattice models, and show how to use them to derive exact properties of field theories by explicit lattice calculations. In the Ising model, the fusion of duality defects allows Kramers-Wannier duality to be enacted on the torus and higher genus surfaces easily, implementing modular invariance directly on the lattice. In other models, the construction leads to generalised dualities previously unknown. A consequence is an explicit definition of twisted boundary conditions that yield the precise shift in momentum quantization and for critical theories, the spin of the associated conformal field. Other universal quantities we compute exactly on the lattice are the ratios of g-factors for conformal boundary conditions
I give an overview of work with Aasen and Mong on topological defects in two-dimensional classical lattice models, quantum spin chains and tensor networks. The partition function in the presence of a topological defect is invariant under any local deformation of the defect. By using results from fusion categories, we construct topological defects in a wide class of lattice models, and show how to use them to derive exact properties of field theories by explicit lattice calculations. In the Ising model, the fusion of duality defects allows Kramers-Wannier duality to be enacted on the torus and higher genus surfaces easily, implementing modular invariance directly on the lattice. In other models, the construction leads to generalised dualities previously unknown. A consequence is an explicit definition of twisted boundary conditions that yield the precise shift in momentum quantization and for critical theories, the spin of the associated conformal field. Other universal quantities we compute exactly on the lattice are the ratios of g-factors for conformal boundary conditions
Posted by: QMW