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Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d

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Referee this paper: arXiv:1404.4385

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

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Summary credit to author Ryan Thorngren

Thought I'd give this a try, especially since Xiao-Gang did as well. :)

I was originally interested in the question of describing boundary topological order for bosonic phases protected by time reversal, though I believe the applications of this sort of investigation are far-reaching in physics. Even though these systems are bosonic, it is known that ``fermionic" things happen in the topological order, eg. Kramers degeneracy and fermionic spin-statistics. This is because the unoriented cobordism invariants, the Stiefel-Whitney classes, are the obstruction classes for things like spin structures. As we go to higher dimensions, what does the topological order--eg. in 3+1d--look like? It turns out to have some sort of fermionic string.

The approach is to think of the unoriented bordism class of spacetime as the configuration of a gauge field. Since this is specified by the Stiefel-Whitney classes, we can consider this as a collection of discrete Z/2 gauge fields in each form degree. Then I define physically the electric and magnetic operators corresponding to such a thing and discuss how they can end.

Some elementary algebraic topology is used to figure out pictorially what it means for a string to be fermionic.

At the end of the paper I show that QED with fermionic electron and fermionic magnetic monopole has a global gravitational anomaly.

summarized by dimension10
paper authored Apr 16, 2014 to hep-th by Ryan Thorngren
  • [ revision history ]
    edited Nov 15, 2014 by dimension10

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