Search Talks

Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface often arise in enumerative problems. We explain how to use the K-theoretic Donaldson-Thomas theory of toric Calabi-Yau threefolds to study K-theoretic versions of such expressions.

Namely, we explicate a precise relationship between K-theoretic Donaldson-Thomas theory and the refined topological vertex of Iqbal, Kosçaz and Vafa. Applying such results to specific toric threefolds, we deduce dualities satisfied by certain generating series that control integrals over the Hilbert scheme of points on a surface. We then explain how to use these dualities to evaluate certain Euler characteristics of tautological bundles on the Hilbert scheme of points on a general surface.

We study the chiral anomaly in disordered Weyl semimetals, where the broken translational symmetry prevents the direct application of Nielsen and Ninomiya’s mechanism and disorder is strong enough that quantum effects are important. In the weak disorder regime, there exists rare regions of the random potential where the disorder strength is locally strong, which gives rise to quasi-localized resonances and their effect on the chiral anomaly is unknown. We numerically show that these resonant states do not affect the chiral anomaly only in the case of a single Weyl node. At energies away from the Weyl point, or with strong disorder where one is deep in the diffusive regime, the chiral Landau level itself is not well defined and the semiclassical treatment is not justified. In this limit, we analytically use the supersymmetry method and find that the Chern-Simons (CS) term in the effective action which is not present in non-topological systems gives rise to a non- zero average level velocity which implies chiral charge pumping. We numerically establish that the non-zero average level velocity serves as an indicator of the chiral anomaly in the diffusive limit. 

In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure. We develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all q-body interactions. We derive the full operator growth structure in the large q limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.

I will present a new method to constrain the quantum effective action of gravity, inspired by recent results from causal dynamical triangulations (CDT). After a short introduction to CDT, I will start from a parameterisation of the effective action to calculate correlation functions for observable quantities. Matching these correlators to CDT data allows to reverse-engineer the couplings which describe the effective dynamics. As a concrete example, the autocorrelation of spatial volume fluctuations is considered. The comparison to CDT data suggests the existence of non-local interaction terms, which might have interesting phenomenological consequences for the interpretation of dark energy.

It is widely known that topological orders have long-range entangled gapped ground states from which nontrivial properties can be extracted. We introduce a new theoretical framework named the information convex, the (convex) set of reduced density matrices of a subsystem in its lowest energy, to characterize topological orders. (1) As a concrete example, we present the calculated topology dependent structure of information convex in the quantum double models and show it reveals properties of bulk anyons and deconfined topological excitations along a gapped boundary, and the condensation rules relating them. (2) As a step towards answering "why the structure of information convex looks that way and whether it has predictive power?" we look into some quantum informational constraints. The topological contribution to von Neumann entropy from each topological excitation type and certain fusion constraints are shown to emerge due to strong subadditivity, assuming fusion multiplicity is encoded in certain topological invariant manner.