Schreiber Anyonic defect branes in TED K-theory

An article that we have written:

  • Hisham Sati\, and \, Urs Schreiber:

    Anyonic Defect Branes and Conformal Blocks in

    Twisted Equivariant Differential (TED) K-Theory

    Reviews in Mathematical Physics

    35 06 (2023) 2350009


    • arXiv:2203.11838

    • pdf (more references added on D 4βŠ₯NS 5⇝M 5βŠ₯M 5D_4 \!\perp\! NS_5 \rightsquigarrow M_5 \!\perp\! M_5 as codim=2 defects; some typose fixed)

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 \mathbb{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 ) \mathrm{SL}(2) -monodromy charges not seen for other branes, at least partially reflected in conformal blocks of the 𝔰𝔩 2^\widehat{\mathfrak{sl}_2}-WZW model over their transverse punctured complex curve. Indeed, it has been argued that all "exotic" branes of string theory are defect branes carrying such U-duality monodromy charges – 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 (β€œinner local systems”) that makes the secondary Chern character on a punctured plane inside an 𝔸 \mathbb{A} -type singularity evaluate to the twisted holomorphic de Rham cohomology which Feigin, Schechtman and Varchenko showed realizes 𝔰𝔩 2^\widehat{\mathfrak{sl}_2}-conformal blocks, here in degree 1 – in fact it gives the direct sum of these over all admissible fractional levels k=βˆ’2+ΞΊ/rk = - 2 + \kappa/r. The remaining higher-degree 𝔰𝔩 2^\widehat{\mathfrak{sl}_2}-conformal blocks appear similarly if we assume our previously discussed β€œHypothesis 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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For more see at Hypothesis H.

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Last revised on May 28, 2024 at 11:56:13. See the history of this page for a list of all contributions to it.