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Already in their early papers, Kosterlitz and Thouless envisaged the melting of solids by the unbinding of the topological defects associated with translational order: dislocations. Later it was realized that the resulting phases have translational symmetry but rotational rigidity: they are liquid crystals.

 

We consider the topological melting of solids as a zero-temperature quantum phase transition. In a generalization of particle-vortex duality, the Goldstone modes of the solid, phonons, map onto gauge bosons which mediate long-range interactions between dislocations. The phase transition is achieved by a Bose-Einstein condensation of dislocations, restoring translational symmetry and destroying shear rigidity. The dual gauge fields become massive due to the Anderson-Higgs mechanism. In this sense, the liquid crystal is a "stress superconductor".

 

We have developed this dual gauge field theory both in 2+1D, where dislocations are particle-like and phonons are vector bosons, and 3+1D where dislocations are string-like and phonons are Kalb-Ramond gauge fields. Focussing mostly on the theoretical formalism, I will discuss the relevance to recent experiments on helium monolayers, which show evidence for a quantum hexatic phase.

 

References:

2+1D : Physics Reports 683, 1 (2017)

3+1D : Physical Review B 96, 1651115 (2017)

In the talk I delineate a simple framework for open science and present empirical results on the adoption of open practices from my own research (+ others). The topics include data sharing, open access infrastructure, and replicability. I will show future perspectives for open science (including knowledge transfer and transdisciplinary research).

To do things together it is not enough to know. We must know what others know, and know that they know we know it, a phenomenon known as Common Knowledge. From the Royal Society to the Science and Nature super-journals, scientists have found ways—however flawed—to achieve it. I’ll introduce the concept of the Artifact, an abstraction that captures the essence of these institutions, and that may help us, in the 21st Century, to go beyond them. And I’ll propose, playfully, a few endeavors that may help us achieve it: Data Mists, Blockchain Republics, and the Moon Shot.

The mathematical definition of Coulomb branches of 3d N=4 gauge theories gives ring objects in the equivariant derived Satake category. We have another fundamental example of a ring object, namely the regular sheaf. It corresponds to the 3d N=4 QFT T[G], studied by Gaiotto-Witten. We also have operations on ring objects, corresponding to products, restrictions, Coulomb/Higgs gauging in the `category' of 3d N=4 QFT's. Thus we conjecture that arbitrary 3d N=4 QFT with G-symmetry gives rise a ring object in the derived Satake for G.