130 research outputs found

### A Symmetry Breaking Scenario for QCD$_3$

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 $N_f\leq 2k$ as well as the dynamics at
$k=0$ we propose that the theory with $N_f> 2k$ breaks the $U(N_f)$ global
symmetry spontaneously to $U(N_f/2+k)\times U(N_f/2-k)$. 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, $2k< N_f< N_*(N,k)$, 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 $SO(N)$ and $Spin(N)$ theories.Comment: 25 pages, 6 figures. v2 added references, minor corrections, new
material about symmetry breaking in U(1) gauge theorie

### Convexity and Liberation at Large Spin

We consider several aspects of unitary higher-dimensional conformal field
theories (CFTs). We first study massive deformations that trigger a flow to a
gapped phase. Deep inelastic scattering in the gapped phase leads to a
convexity property of dimensions of spinning operators of the original CFT. We
further investigate the dimensions of spinning operators via the crossing
equations in the light-cone limit. We find that, in a sense, CFTs become free
at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys
additivity: if two twists tau_1, tau_2 appear in the spectrum, there are
operators whose twists are arbitrarily close to tau_1+tau_2. We characterize
how tau_1+tau_2 is approached at large spin by solving the crossing equations
analytically. We find the precise form of the leading correction, including the
prefactor. We compare with examples where these observables were computed in
perturbation theory, or via gauge-gravity duality, and find complete agreement.
The crossing equations show that certain operators have a convex spectrum in
twist space. We also observe a connection between convexity and the ratio of
dimension to charge. Applications include the 3d Ising model, theories with a
gravity dual, SCFTs, and patterns of higher spin symmetry breaking.Comment: 61 pages, 13 figures. v2: added reference and minor correctio

### Cardy Formulae for SUSY Theories in d=4 and d=6

We consider supersymmetric theories on a space with compact space-like
slices. One can count BPS representations weighted by (-1)^F, or, equivalently,
study supersymmetric partition functions by compactifying the time direction. A
special case of this general construction corresponds to the counting of short
representations of the superconformal group. We show that in four-dimensional
N=1 theories the "high temperature" asymptotics of such counting problems is
fixed by the anomalies of the theory. Notably, the combination a-c of the trace
anomalies plays a crucial role. We also propose similar formulae for
six-dimensional (1,0) theories.Comment: 33 pages; added reference

### Curious Aspects of Three-Dimensional ${\cal N}=1$ SCFTs

We study the dynamics of certain 3d ${\cal N}=1$ time reversal invariant
theories. Such theories often have exact moduli spaces of supersymmetric vacua.
We propose several dualities and we test these proposals by comparing the
deformations and supersymmetric ground states. First, we consider a theory
where time reversal symmetry is only emergent in the infrared and there exists
(nonetheless) an exact moduli space of vacua. This theory has a dual
description with manifest time reversal symmetry. Second, we consider some
surprising facts about ${\cal N}=2$ $U(1)$ gauge theory coupled to two chiral
superfields of charge 1. This theory is claimed to have emergent $SU(3)$ global
symmetry in the infrared. We propose a dual Wess-Zumino description (i.e. a
theory of scalars and fermions but no gauge fields) with manifest $SU(3)$
symmetry but only ${\cal N}=1$ supersymmetry. We argue that this Wess-Zumino
model must have enhanced supersymmetry in the infrared. Finally, we make some
brief comments about the dynamics of ${\cal N}=1$ $SU(N)$ gauge theory coupled
to $N_f$ quarks in a time reversal invariant fashion. We argue that for $N_f<N$
there is a moduli space of vacua to all orders in perturbation theory but it is
non-perturbatively lifted.Comment: 30 pages, 4 figures v2: references adde

### Sphere Partition Functions and the Zamolodchikov Metric

We study the finite part of the sphere partition function of d-dimensional
Conformal Field Theories (CFTs) as a function of exactly marginal couplings. In
odd dimensions, this quantity is physical and independent of the exactly
marginal couplings. In even dimensions, this object is generally regularization
scheme dependent and thus unphysical. However, in the presence of additional
symmetries, the partition function of even-dimensional CFTs can become
physical. For two-dimensional N=(2,2) supersymmetric CFTs, the continuum
partition function exists and computes the Kahler potential on the chiral and
twisted chiral superconformal manifolds. We provide a new elementary proof of
this result using Ward identities on the sphere. The Kahler transformation
ambiguity is identified with a local term in the corresponding N=(2,2)
supergravity theory. We derive an analogous, new, result in the case of
four-dimensional N=2 supersymmetric CFTs: the S^4 partition function computes
the Kahler potential on the superconformal manifold. Finally, we show that N=1
supersymmetry in four dimensions and N=(1,1) supersymmetry in two dimensions
are not sufficient to make the corresponding sphere partition functions
well-defined functions of the exactly marginal parameters.Comment: 32 pages; added references and minor correction

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