Talks

I will review recent and ongoing developments in path integral optimization and path integral complexity in 2d CFTs. After, I will discuss the connection with geometric approach to circuit complexity and point out several open problems.

Interacting electrons in high magnetic fields exhibit rich physical phenomena including the gapped fractional quantum Hall effects and the gapless states. The composite Fermi liquids (CFLs) are gapless states that can occur at even denominator Landau level fillings. Due to the celebrated work of Halperin, Lee and Read (94), the CFLs were understood as Fermi liquids of composite fermions, which are bound states of electron and electromagnetic flux quanta. However, at 1/2 filling, it is not obvious why the HLR description is consistent with the particle hole symmetry. Motivated by this, recently Son (15) proposed an alternative description for CFLs at 1/2, according to which the composite fermions are instead emergent Dirac fermions. Importantly, Son’s theory predicts a Pi Berry curvature singularity at the composite Fermi sea center. In the first part of this talk [2,3], I will present our numerical work about detecting this Z2 Berry phase at 1/2 filling. In the second part [1], I will present how and why Dirac fermions can emerge at all the other filling fractions (1/2m and 1-1/2m when m is integer) even without the particle hole symmetry.

[1] arXiv 1808.07529. JW.

[2] arXiv 1711.07864. Geraedts, JW, Rezayi, Haldane.

[3] arXiv 1710.09729. JW, Geraedts, Rezayi, Haldane.

Anomaly cancellation conditions place strong constraints on many physical theories. In the traditional framework, local and global anomalies are detected by computing an eta invariant of a certain Dirac operator on a mapping torus. Recent research has uncovered the existence of finer anomaly cancellation conditions, not visible in these traditional settings. I will review the traditional and refined anomalies, and apply them to various symmetries of interest in particle physics. Examples include the (various global forms of) the Standard Model, GUT's, and discrete gauge symmetries of physical interest such as proton triality and a certain Z4 symmetry in the (MS)SM.

The Twin Higgs model is an attractive solution to the little Hierarchy problem with top partners that are neutral under SM gauge charges. The framework is consistent with the null result of LHC colored top partner searches while offering many alternative discovery channels. Depending on model details, the phenomenology looks very different: either spectacular long-lived particle signals at colliders, or a plethora of unusual cosmological and astrophysical signatures via the existence of a predictive hidden sector. I will examine the latter possibility, and describe how the asymmetrically reheated Mirror Twin Higgs provides a predictive framework for a highly motivated and highly non-trivial interacting dark sector, with correlated signals in the CMB, Large Scale Structure, and direct detection searches, as well as higgs precision measurements at colliders. This provides a vivid example of the collider-cosmology complementarity, and motivates a variety of new astrophysical searches that are motivated by the hierarchy problem.

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.