Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and ...demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.
A symmetry breaking scenario for QCD3 Komargodski, Zohar; Seiberg, Nathan
The journal of high energy physics,
01/2018, Letnik:
2018, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A
bstract
We consider the dynamics of 2+1 dimensional SU(
N
) gauge theory with Chern-Simons level
k
and
N
f
fundamental fermions. By requiring consistency with previously suggested dualities for
N
f
...≤ 2
k
as well as the dynamics at
k
= 0 we propose that the theory with
N
f
>
2
k
breaks the U(
N
f
) global symmetry spontaneously to U(
N
f
/
2 +
k
) × U(
N
f
/
2 −
k
). In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, 2
k < N
f
< N
∗
(
N, k
), with the upper limit
N
∗
obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at
k
= 0. Furthermore, we suggest two scalar dual theories in this range of
N
f
. A similar picture is developed for SO(
N
) and Sp(
N
) gauge theories. It sheds new light on monopole condensation and confinement in the SO(
N
) & Spin(
N
) theories.
We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime
, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler ...than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For
we reproduce the known results in the literature. A supersymmetric Lagrangian for
exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for
and note that the time direction
can be rotated to Euclidean signature and be compactified to
only when the theory has a continuous R-symmetry. The partition function on
is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant
theories on
and clarify a few points about them.
Theta, time reversal and temperature Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar ...
The journal of high energy physics,
05/2017, Letnik:
2017, Številka:
5
Journal Article
Recenzirano
Odprti dostop
A
bstract
SU(
N
) gauge theory is time reversal invariant at
θ
= 0 and
θ
=
π
. We show that at
θ
=
π
there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly ...leads to constraints on the vacua of the theory. It follows that at
θ
=
π
the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at
θ
= 0 is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at
θ
=
π
, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for SU(2) gauge theory. The underlying symmetry at
θ
=
π
is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two
O
(2)-symmetric fixed points. It may also be that the four-dimensional theory around
θ
=
π
is gapless, e.g. a Coulomb phase could match the underlying anomalies.
A
bstract
We study SU(
N
) Quantum Chromodynamics (QCD) in 3+1 dimensions with
N
f
degenerate fundamental quarks with mass
m
and a
θ
-parameter. For generic
m
and
θ
the theory has a single gapped ...vacuum. However, as
θ
is varied through
θ
=
π
for large
m
there is a first order transition. For
N
f
= 1 the first order transition line ends at a point with a massless
η
′ particle (for all
N
) and for
N
f
>
1 the first order transition ends at
m
= 0, where, depending on the value of
N
f
, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4
d
bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3
d
phases. These turn out to be the phases of the recently studied 3
d
Chern-Simons matter theories, thus relating the dynamics of QCD
4
and QCD
3
, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4
d
theory has an SU(
N
f
) sigma model, the domain wall theory at low (nonzero) mass supports a 3
d
massless
ℂ
ℙ
N
f
−
1
nonlinear
σ
-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.
A
bstract
We analyze in detail the global symmetries of various (2 + 1)
d
quantum field theories and couple them to classical background gauge fields. A proper identification of the global symmetries ...allows us to consider all non-trivial bundles of those background fields, thus finding more subtle observables. The global symmetries exhibit interesting ’t Hooft anomalies. These allow us to constrain the IR behavior of the theories and provide powerful constraints on conjectured dualities.
The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual
θ
...-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer
p
. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kähler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of ...systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.
We extend our exploration of nonstandard continuum quantum field
theories in
2+1
2
+
1
dimensions to
3+1
3
+
1
dimensions. These theories exhibit exotic global symmetries, a peculiar
spectrum of ...charged states, unusual gauge symmetries, and surprising
dualities. Many of the systems we study have a known lattice
construction. In particular, one of them is a known gapless fracton
model. The novelty here is in their continuum field theory description.
In this paper, we focus on models with a global
U(1)
U
(
1
)
symmetry and in a followup paper we will study models with a global
\mathbb{Z}_N
ℤ
N
symmetry.
Abstract
The standard boundary state of a topological insulator in 3 + 1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one ...phase, but also have gapped phases with topological order. Our models are weakly coupled and all the dynamics is explicit. We rederive some known boundary states of topological insulators and construct new ones. Consistency with the standard spin/charge relation of condensed matter physics places a nontrivial constraint on models.
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