20.01.2022 (Thursday)

Relative Defects and Trapped Higher-Form Symmetries

Journal Club Lakshya Bhardwaj (Oxford)

at:
12:00 QMW
room G.O. Jones 610
abstract:

Relative theories are non-topological theories living at the boundaries of TQFTs in one higher dimension. An interesting and well-studied class of relative theories are 6d N=(2,0) theories. I will introduce the notion of relative defects in relative theories, which are non-topological defects of the relative theory living at the boundary of a topological defect of the above-mentioned TQFT in one higher dimension. I will argue that codimension two defects of 6d N=(2,0) theories are relative defects. Relative defects carry ''trapped'' higher-form symmetries localized on their world-volume which are independent from the higher-form symmetries of the bulk theory. When the bulk theory is compactified with the insertion of relative defects, the trapped higher-form symmetries provide extra contributions to the higher-form symmetries of the lower-dimensional theory resulting from the compactification. For example, when 6d N=(2,0) theories are compactified on a Riemann surfaces with punctures (which are relative codimension-two defects) then the 1-form symmetry of the resulting 4d N=2 Class S theory obtains contributions from the 1-form symmetries trapped at the punctures, along with the well-known contribution coming from the 2-form symmetry of the 6d N=(2,0) theory; part of London TQFT Journal Club; it will be possible to follow this talk on Zoom (please register at https://london-tqft.vercel.app)