We study in general spacetime dimension the symmetry of the theory
obtained by gauging a non-anomalous finite normal Abelian subgroup
A
A
of a
\Gamma
Γ
-symmetric
theory. Depending on how anomalous
...\Gamma
Γ
is, we find that the symmetry of the gauged theory can be i) a direct
product of
G=\Gamma/A
G
=
Γ
/
A
and a higher-form symmetry
\hat A
A
̂
with a mixed anomaly, where
\hat A
A
̂
is the Pontryagin dual of
A
A
;
ii) an extension of the ordinary symmetry group
G
G
by the higher-form symmetry
\hat A
A
̂
;
iii) or even more esoteric types of symmetries which are no longer
groups. We also discuss the relations to the effect called the
H^3(G,\hat A)
H
3
(
G
,
A
̂
)
symmetry localization obstruction in the condensed-matter theory and to
some of the constructions in the works of Kapustin-Thorngren and
Wang-Wen-Witten.
A
bstract
The anomaly polynomial of a theory can involve not only curvature two-forms of the flavor symmetry background but also two-forms on the space of coupling constants. As an example, we point ...out that there is a mixed anomaly between the R-symmetry and the topology of the space of exactly marginal couplings of class S theories. Using supersymmetry, we translate this anomaly to the Kähler class of the Zamolodchikov metric. We compare the result against a holographic computation in the large
N
limit.
A
bstract
It is well-known that if we gauge a ℤ
n
symmetry in two dimensions, a dual ℤ
n
symmetry appears, such that re-gauging this dual ℤ
n
symmetry leads back to the original theory. We describe ...how this can be generalized to non-Abelian groups, by enlarging the concept of symmetries from those defined by groups to those defined by unitary fusion categories. We will see that this generalization is also useful when studying what happens when a non-anomalous subgroup of an anomalous finite group is gauged: for example, the gauged theory can have non-Abelian group symmetry even when the original symmetry is an Abelian group. We then discuss the axiomatization of two-dimensional topological quantum field theories whose symmetry is given by a category. We see explicitly that the gauged version is a topological quantum field theory with a new symmetry given by a dual category.
A
bstract
We study higher symmetries and anomalies of 4d
so
(2
n
c
) gauge theory with 2
n
f
flavors. We find that they depend on the parity of
n
c
and
n
f
, the global form of the gauge group, and ...the discrete theta angle. The contribution from the fermions plays a central role in our analysis. Furthermore, our conclusion applies to
N
= 1 supersymmetric cases as well, and we see that higher symmetries and anomalies match across the Intriligator-Seiberg duality between
so
(2
n
c
)
↔
so
(2
n
f
− 2
n
c
+ 4).
Abstract
Spacetime theories obtained from perturbative string theory constructions are automatically free of perturbative anomalies, but it is not settled whether they are always free of global ...anomalies. Here we discuss a possible $\mathbb{Z}_{24}$-valued pure gravitational anomaly of heterotic compactifications down to two spacetime dimensions, and point out that it can be shown to vanish using the theory of topological modular forms, assuming the validity of the Stolz–Teichner conjecture.
A
bstract
We revisit the
N
= 6 superconformal Chern-Simons-matter theories and their supergravity duals in the context of generalized symmetries. This allows us to finally clarify how the SU(
N
)
×
...SU(
N
) and (SU(
N
)
×
SU(
N
))
/
ℤ
N
theories, as well as other quotient theories that have recently been discussed, fit into the holographic framework. It also resolves a long standing puzzle regarding the di-baryon operator in the U(
N
)
×
U(
N
) theory.
A
bstract
We consider an analogue of Witten’s SL(2
,
ℤ) action on three-dimensional QFTs with U(1) symmetry for 2
k
-dimensional QFTs with ℤ
2
(
k −
1)-form symmetry. We show that the SL(2
,
ℤ) ...action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the SL(2
,
ℤ) anomaly of the bulk (2
k
+ 1)-dimensional ℤ
2
gauge theory.
We prove an explicit formula conjectured recently by Wang and Levin for the anomaly of time-reversal symmetry in (2+1)-dimensional fermionic topological quantum field theories. The crucial step is to ...determine the cross-cap state in terms of the modular S matrix and T^{2} eigenvalues, generalizing the recent analysis by Barkeshli et al. in the bosonic case.
A
bstract
We introduce autoboot, a Mathematica program which automatically generates mixed correlator bootstrap equations of an arbitrary number of scalar external operators, given the global ...symmetry group and the representations of the operators. The output is a Python program which uses Ohtsuki’s cboot which in turn uses Simmons-Duffin’s sdpb. The code is available at
https://github.com/selpoG/autoboot/
.
In an appendix we also discuss a simple technique to significantly reduce the time to run sdpb, which we call hot-starting.
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