Talks

Symplectic duality predicts that symplectic singularities should come in pairs. For example, Nakajima quiver varieties are conjecturally dual to BFN Coulomb branches (of the corresponding quiver theories). Another family of potentially symplectically dual pairs was described recently in the works of Losev, Mason-Brown, and Matvieievskyi: they describe symplectically duals to Slodowy slices to nilpotent orbits.

In this talk, we will discuss the Hikita-Nakajima conjecture that relates the geometry of symplectically dual varieties. We will restrict to the cases of certain quiver varieties and Slodowy slices and discuss the picture in these cases.

Based on the joint work with Pavel Shlykov (arXiv:2202.09934) and the work in progress with Do Kien Hoang and Dmytro Matvieievskyi.

Zoom link:  https://pitp.zoom.us/j/98651907502?pwd=ODA1K3NKVHFLdkp6TEtaSnJXdThVZz09

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT.  This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity.  Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes.  These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory  Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.  Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge mode

Zoom link:  https://pitp.zoom.us/j/98275430953?pwd=TzdTUXIvVWU4Ym1jcWRWbkgxZnhMdz09

Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the spurious topological entanglement entropy. We show this spurious contribution is always nonnegative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE which is invariant under constant-depth quantum circuits.

Based on a joint work with Daniel Ranard (MIT), Michael Levin (U Chicago), Ting-Chun Lin (UCSD), and Bowen Shi (UCSD)

Zoom link:  https://pitp.zoom.us/j/93809342984?pwd=QXJkK0ZYR3QzdjlUUWlkMEFXMWRnQT09

In massless QED, we find that the classical U(1) axial symmetry is not completely broken by the Adler-Bell-Jackiw anomaly. Rather, it is resurrected as a generalized global symmetry labeled by the rational numbers. Intuitively, this new global symmetry in QED is a composition of the naive axial rotation and a fractional quantum Hall state. The conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra. We further generalize our construction to QCD, and show that the neutral pion decay can be derived from a matching condition of the non-invertible global symmetry. Finally, we find a non-invertible Gauss law in axion-Maxwell theory.

Zoom link:  https://pitp.zoom.us/j/93832561140?pwd=czFFSkVvYS9RbXRjOTJPQVFhL2hGZz09