Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant
Differential (TED) K-theory
- URL: http://arxiv.org/abs/2203.11838v1
- Date: Tue, 22 Mar 2022 16:05:58 GMT
- Title: Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant
Differential (TED) K-theory
- Authors: Hisham Sati, Urs Schreiber
- Abstract summary: We show that twisted equivariant differential K-theory accommodates exotic charges of the form expected of codimension=2 defect branes.
This provides a concrete first-principles realization of anyon statistics of -- and hence of topological quantum computation on -- defect branes in string/M-theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We demonstrate that twisted equivariant differential K-theory of transverse
complex curves accommodates exotic charges of the form expected of
codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type
orbifold singularities, but also of their dual 3-brane defects of class-S
theories on M5-branes. These branes have been argued, within F-theory and the
AGT correspondence, to carry special SL(2)-monodromy charges not seen for other
branes, but none of these had previously been identified in the expected brane
charge quantization law given by K-theory.
Here we observe that it is the subtle (and previously somewhat neglected)
twisting of equivariant K-theory by flat complex line bundles appearing inside
orbi-singularities ("inner local systems") that makes the secondary Chern
character on a punctured plane inside an A-type singularity evaluate to the
twisted holomorphic de Rham cohomology which Feigin, Schechtman & Varchenko
showed realizes sl(2,C)-conformal blocks, here in degree 1 -- in fact it gives
the direct sum of these over all admissible fractional levels. The remaining
higher-degree conformal blocks appear similarly if we assume our previously
discussed "Hypothesis H" about brane charge quantization in M-theory. Since
conformal blocks -- and hence these twisted equivariant secondary Chern
characters -- solve the Knizhnik-Zamolodchikov equation and thus constitute
representations of the braid group of motions of defect branes inside their
transverse space, this provides a concrete first-principles realization of
anyon statistics of -- and hence of topological quantum computation on --
defect branes in string/M-theory.
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