A
bstract
We discuss consequences of the ’t Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete ’t Hooft anomaly of massless ...QCD for generic numbers of color
N
c
and flavor
N
f
, and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the U(1)
B
baryon number symmetry is anomalously broken when the
ℤ
2
N
f
A
discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmetry breaking, the Skyrmion current turns out to reproduce this ’t Hooft anomaly of massless QCD. In the exotic chiral symmetry breaking, however, the anomalous breaking of U(1)
B
does not take the correct form, and it is inconsistent with anomaly matching. This no-go theorem is based only on symmetries and anomalies, and thus has a wider range of applicability to the QCD phase diagram than the previous one obtained by QCD inequalities. Lastly, as another application, we check that duality of
N
=
1
supersymmetric QCD with
N
f
≥
N
c
+ 1 satisfies the new anomaly matching.
A
bstract
We consider the SU(
N
) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of
p
. We can formulate such a quantum field theory ...maintaining locality and unitarity, and the model contains both 2
π
-periodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ℤ
N
1-form symmetry but also ℤ
p
3-form symmetry, and we study the global nature of this theory from the recent ’t Hooft anomaly matching. The computation of ’t Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large-
N
and also the reliable semiclassics on ℝ
3
×
S
1
, and we find that the topological susceptibility plays a role of the order parameter for the ℤ
p
3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by ℤ
p
, and it leads to the extra
p
vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the ’t Hooft anomaly.
A
bstract
We study a 3d lattice gauge theory with gauge group U(1)
N−
1
⋊ S
N
, which is obtained by gauging the S
N
global symmetry of a pure U(1)
N−
1
gauge theory, and we call it the semi-Abelian ...gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(
N
) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤ
N
, we observe that the string tensions do not obey the
N
-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)
N−
1
one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to
W
-bosons, such non-invertible symmetries are explicitly broken so that the
N
-ality rule should emerge in the deep infrared regime.
A
bstract
We discuss possible vacuum structures of SU(
n
) × SU(
n
) gauge theories with bifundamental matters at finite
θ
angles. In order to give a precise constraint, a mixed ’t Hooft anomaly is ...studied in detail by gauging the center
ℤ
n
one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the con-straints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.
A
bstract
We study a four-dimensional U(1) gauge theory with the
θ
angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the ...presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at
θ
=
π
, and show how its appearance can be consistent with the anomaly constraint. We also construct the SL(2
,
ℤ) self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed ’t Hooft anomaly with gravity, and its implications on the phase diagram is uncovered. As the model shares the same global symmetry and ’t Hooft anomaly with those of SU(
N
) Yang-Mills theory, studying its topological aspects would provide us more hints to explore possible dynamics of non-Abelian gauge theories with nonzero
θ
angles.
A
bstract
We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2
...,
ℤ) self-duality at low-energies. SL(2
,
ℤ) self-duality does not realize in a naive way, but we notice that the
ST
p
duality transformation becomes the legitimate duality operation by performing the gauging of ℤ
N
1-form symmetry with including the level-
p
discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a
K
3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.
Circle compactification and ’t Hooft anomaly Tanizaki, Yuya; Misumi, Tatsuhiro; Sakai, Norisuke
The journal of high energy physics,
12/2017, Letnik:
2017, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
Anomaly matching constrains low-energy physics of strongly-coupled field theories, but it is not useful at finite temperature due to contamination from high-energy states. The known ...exception is an ’t Hooft anomaly involving one-form symmetries as in pure SU(
N
) Yang-Mills theory at
θ
=
π
. Recent development about large-
N
volume independence, however, gives us a circumstantial evidence that ’t Hooft anomalies can also remain under circle compactifications in some theories without one-form symmetries. We develop a systematic procedure for deriving an ’t Hooft anomaly of the circle-compactified theory starting from the anomaly of the original uncompactified theory without one-form symmetries, where the twisted boundary condition for the compactified direction plays a pivotal role. As an application, we consider
ℤ
N
-twisted
ℂ
P
N
−
1
sigma model and massless
ℤ
N
-QCD, and compute their anomalies explicitly.
A
bstract
This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-
q N
...-flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on ℝ
2
and its compactification to ℝ×
S
L
1
. We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are
Nq
vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional
θ
dependence e
i
θ
/
Nq
, which provides the
Nq
-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-
N
limit of the Schwinger model with twisted boundary conditions satisfy volume independence.
A
bstract
We study low-energy dynamics of SU(
N
)
K
chiral quiver gauge theories in connection with
N
= 1 super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions ...(QCD(BF)). These theories can be obtained by ℤ
K
orbifold projections of
N
= 1 SU(
N K
) SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for
K ≥
3. In order to study low-energy behaviors, we analyze these systems using ’t Hooft anomaly matching and reliable semiclassics on ℝ
3
× S
1
. Thanks to ’t Hooft anomaly that involves 1-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist
N
vacua. Theories with even
K
possess a physical
θ
angle despite the presence of massless fermions, and we further predict the
N
-branch structure associated with it; the number of vacua is enhanced to 2
N
at
θ
=
π
due to spontaneous
C P
breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on R
3
× S
1
with the double-trace deformation. Symmetry and anomaly of odd-
K
theories are the same as those of the
N
= 1 SYM, and the ones of even-
K
theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.
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