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Self-duality under gauging a non-invertible symmetry
Ist Teil von
The journal of high energy physics, 2024-01, Vol.2024 (1), p.142-55, Article 142
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2024
Quelle
EZB Electronic Journals Library
Beschreibungen/Notizen
A
bstract
We discuss two-dimensional conformal field theories (CFTs) which are invariant under gauging a non-invertible global symmetry. At every point on the orbifold branch of
c
= 1 CFTs, it is known that the theory is self-dual under gauging a ℤ
2
× ℤ
2
symmetry, and has Rep(
H
8
) and Rep(
D
8
) fusion category symmetries as a result. We find that gauging the entire Rep(
H
8
) fusion category symmetry maps the orbifold theory at radius
R
to that at radius 2/
R
. At
R
=
2
, which corresponds to two decoupled Ising CFTs (Ising
2
in short), the theory is self-dual under gauging the Rep(
H
8
) symmetry. This implies the existence of a topological defect line in the Ising
2
CFT obtained from half-space gauging of the Rep(
H
8
) symmetry, which commutes with the
c
= 1 Virasoro algebra but does not preserve the fully extended chiral algebra. We bootstrap its action on the
c
= 1 Virasoro primary operators, and find that there are no relevant or marginal operators preserving it. Mathematically, the new topological line combines with the Rep(
H
8
) symmetry to form a bigger fusion category which is a ℤ
2
-extension of Rep(
H
8
). We solve the pentagon equations including the additional topological line and find 8 solutions, where two of them are realized in the Ising
2
CFT. Finally, we show that the torus partition functions of the Monster
2
CFT and Ising
×
Monster CFT are also invariant under gauging the Rep(
H
8
) symmetry.