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 symmetry breaking scenario for QCD3 Komargodski, Zohar; Seiberg, Nathan
The journal of high energy physics,
01/2018, Volume:
2018, Issue:
1
Journal Article
Peer reviewed
Open access
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.
A
bstract
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of ...Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities.
6D SCFTs and phases of 5D theories Del Zotto, Michele; Heckman, Jonathan J.; Morrison, David R.
The journal of high energy physics,
09/2017, Volume:
2017, Issue:
9
Journal Article
Peer reviewed
Open access
A
bstract
Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D ...theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.
A
bstract
We consider Chern-Simons theory for gauge group
G
at level
k
on 3-manifolds
M
n
with boundary consisting of
n
topologically linked tori. The Euclidean path integral on
M
n
defines a quantum ...state on the boundary, in the
n
-fold tensor product of the torus Hilbert space. We focus on the case where
M
n
is the link-complement of some
n
-component link inside the three-sphere
S
3
. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level
k
(
G
= U(1)
k
) we give a general formula for the entanglement entropy associated to an arbitrary (
m
|
n
−
m
) partition of a generic
n
-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod
k
) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod
k
). For
G
= SU(2)
k
, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a “W-like” entanglement structure (i.e., tracing out one torus does
not
lead to a separable state), and give examples of other 3-component links which have “GHZ-like” entanglement (i.e., tracing out one torus
does
lead to a separable state).
A
bstract
We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant det
T
of the stress tensor, commonly referred to as
T
T
¯
. ...Infinitesimally this is equivalent to a random coordinate transformation, with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology. We discuss in detail the examples of a torus, a finite cylinder, a disk and a more general simply connected domain. In all cases the partition function evolves according to a linear diffusion-type equation, and the deformation may be viewed as a kind of random walk in moduli space. We also discuss possible generalizations to higher dimensions.
A
bstract
We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path ...integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a “fluid spacetime” and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional
Z
2
symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.
Massive gravity from double copy Momeni, Arshia; Rumbutis, Justinas; Tolley, Andrew J.
The journal of high energy physics,
12/2020, Volume:
2020, Issue:
12
Journal Article
Peer reviewed
Open access
A
bstract
We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low ...energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ
3
= (
m
2
M
Pl
)
1
/
3
cutoff. We construct explicitly the Λ
3
decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ
3
massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.
A
bstract
We consider the conformal field theory of
N
complex massless scalars in 2 + 1 dimensions, coupled to a U(
N
) Chern-Simons theory at level
k
. This theory has a ’t Hooft large
N
limit, ...keeping fixed λ ≡
N
/
k
. We compute some correlation functions in this theory exactly as a function of λ, in the large
N
(planar) limit. We show that the results match with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large
N
limit. It has been suggested in the past that this theory is dual (in the large
N
limit) to the Legendre transform of the theory of fermions coupled to a Chern-Simons gauge field, and our results allow us to find the precise mapping between the two theories. We find that in the large
N
limit the theory of
N
scalars coupled to a U(
N
)
k
Chern-Simons theory is equivalent to the Legendre transform of the theory of
k
fermions coupled to a U(
k
)
N
Chern-Simons theory, thus providing a bosonization of the latter theory. We conjecture that perhaps this duality is valid also for finite values of
N
and
k
, where on the fermionic side we should now have (for
N
f
flavors) a
theory. Similar results hold for real scalars (fermions) coupled to the
O
(
N
)
k
Chern-Simons theory.
A
bstract
It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of ...gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of
twist vortices
: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.
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