I plan to use the introduction to review some past work on emergent symmetries. But then in the spirit of the workshop I will describe some ongoing work on a pathway to describe why general relativity appears as a metric theory, without initially making that assumption.
Maximal Entanglement appears to be a key ingredient for the emergence
of symmetries. We first illustrate this phenomenon using two examples:
the emergence of conformal symmetry in condensed matter systems
and the relation of tensor networks to holography. We further present
a Principle of Maximal Entanglement that seems to dictate to a large
extend the structure of gauge symmetry.
Holography allows us to formulate questions about quantum gravity in terms of more ordinary quantum field theories without gravity. A natural and long-standing goal has been to understand the physics of black holes using holographic duality. I will report on some recent progress on this question formulating the spherical collapse of an in-falling shell of null matter in three dimensions in...
We consider QFT in hyperbolic space and study correlation functions of operators inserted at the conformal boundary. By construction, these observables transform like correlation functions of a lower dimensional Conformal Field Theory. We then apply conformal bootstrap techniques to find universal bounds on the mass spectrum and scattering amplitudes of the QFT. The AdS/CFT correspondence...
We reformulate the O(2) model with a chemical potential and the Abelian Higgs model using the
Tensor Renormalization Group method (both on a 1+1 space-time lattice).
The reformulation allows exact blocking, is manifestly gauge invariant and connects smoothly the classical Lagrangian formulation
used by lattice gauge theorists to the quantum Hamiltonian method commonly used in condensed...
I will review recent work on quantum criticality in three-dimensional gapless semiconductors, which feature quadratic band crossing at the fermi level. These rather ubiquitous systems, such as gray tin and mercury telluride, feature only a Galilean (z=2) invariance at low energies, and should exhibit interesting new phases and transitions as a result of electron-electron and electron-phonon...
I will discuss a proof of bounds for central charges in unitary CFTs using crossing symmetry and its implication for the average null energy condition.
By enforcing suitable relations associated to the Poincar\'e invariance
of the continuum theory, it is possible to define an energy-momentum
tensor on the lattice which satisfies the appropriate Ward Identites and
has the right trace anomaly in the continuum limit. The renormalization
conditions come forth when the length of the box in the temporal direction
is finite, and they take a...
Some non-abelian gauge theories coupled with many massless fermions show the conformal behavior in the low energy limit.
The range of the number of fermions, where the theory has the nontrivial infrared fixed point, is called “conformal window".
Recent lattice studies confirm the existence of the conformal window from the first-principle calculation, and clarify those conformal properties,...
