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This is a standard particle-vortex duality transformation. The idea is there exists a "dual" description of a superfluid, in which the bosons (to be precise, the Goldstone mode) is described by a 2-form(tensor) gauge field, and the vortices are now string-like "matter" charged under the gauge field. The effective action for phase fluctuations (i.e. Goldstone ...


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If your spacetime is compact and if every point has an open neighborhood that locally looks like special relativity, then it contains closed timelike curves (aka time travel). The argument is standard math. For each point p, there is an open neighborhood that looks like SR and hence contains points q in p's causal past. So the set of causal futures of ...


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Intuitively this actually is very plausible, though you have to work your intuition a bit; fix a point in configuration space, this can be seen as a single point in something that locally looks like $\Bbb R^{2n}$ or $\Bbb R^{3n}$, but it is more convenient to think of $n$ distinct points of (something that locally looks like) $\Bbb R^2$ or $\Bbb R^3$. A ...


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I guess you have to read this in the context of intersection theory. On a manifold of dimension $2n$ we have the $n$-th homology group, which can informally be thought of as being generated by equivalence classes of $n$-dimensional submanifolds. Intersecting two of these should generally give a discrete set of points. Intuitively the intersection product can ...



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