91 research outputs found
Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
We study 3d and 4d systems with a one-form global symmetry, explore their
consequences, and analyze their gauging. For simplicity, we focus on
one-form symmetries. A 3d topological quantum field theory
(TQFT) with such a symmetry has special lines that generate
it. The braiding of these lines and their spins are characterized by a single
integer modulo . Surprisingly, if the TQFT factorizes
. Here is a
decoupled TQFT, whose lines are neutral under the global symmetry and
is a minimal TQFT with the one-form symmetry
of label . The parameter labels the obstruction to gauging the
one-form symmetry; i.e.\ it characterizes the 't Hooft anomaly
of the global symmetry. When mod , the symmetry can be gauged.
Otherwise, it cannot be gauged unless we couple the system to a 4d bulk with
gauge fields extended to the bulk. This understanding allows us to consider
and 4d gauge theories. Their dynamics is gapped and it is
associated with confinement and oblique confinement -- probe quarks are
confined. In the theory the low-energy theory can include a discrete
gauge theory. We will study the behavior of the theory with a space-dependent
-parameter, which leads to interfaces. Typically, the theory on the
interface is not confining. Furthermore, the liberated probe quarks are anyons
on the interface. The theory is obtained by gauging the
one-form symmetry of the theory. Our understanding of the symmetries in
3d TQFTs allows us to describe the interface in the theory.Comment: 56 pages, 3 figures, 5 table
Ground State Degeneracy of Infinite-Component Chern-Simons-Maxwell Theories
Infinite-component Chern-Simons-Maxwell theories with a periodic matrix
provide abundant examples of gapped and gapless, foliated and non-foliated
fracton orders. In this paper, we study the ground state degeneracy of these
theories. We show that the ground state degeneracy exhibit various patterns as
a function of the linear system size -- the size of the matrix. It can grow
exponentially or polynomially, cycle over finitely many values, or fluctuate
erratically inside an exponential envelope. We relate these different patterns
of the ground state degeneracy with the roots of the ``determinant
polynomial'', a Laurent polynomial, associated to the periodic matrix.
These roots also determine whether the theory is gapped or gapless. Based on
the ground state degeneracy, we formulate a necessary condition for a gapped
theory to be a foliated fracton order.Comment: 15 pages, 1 figure; the authors are ordered alphabeticall
Non-invertible Time-reversal Symmetry
In gauge theory, it is commonly stated that time-reversal symmetry only
exists at or for a -periodic -angle. In this
paper, we point out that in both the free Maxwell theory and massive QED, there
is a non-invertible time-reversal symmetry at every rational -angle,
i.e., . The non-invertible time-reversal symmetry is
implemented by a conserved, anti-linear operator without an inverse. It is a
composition of the naive time-reversal transformation and a fractional quantum
Hall state. We also find similar non-invertible time-reversal symmetries in
non-Abelian gauge theories, including the super
Yang-Mills theory along the locus on the conformal manifold.Comment: 30 page
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