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

A Symmetry Breaking Scenario for QCD3_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

Non-Supersymmetric Brane Configurations, Seiberg Duality and Dynamical Symmetry Breaking

We consider type IIA brane configurations, similar to those that realize SO(2N) supersymmetric QCD, that include orientifold planes and anti-branes. Such brane configurations lead to Sp(2N) field theories that become supersymmetric in the large-N limit and break supersymmetry upon the inclusion of 1/N corrections. We argue that this class of field theories admit Seiberg duality and interpret the potential between branes and orientifolds as field theory phenomena. In particular we find in the magnetic theory a meson potential that leads to dynamical symmetry breaking and a meson condensate similar to the anticipated quark condensate in QCD.Comment: 22 pages. LaTex. 5 eps figures. v2: minor changes, reference and a comment about the GMOR relation added. To appear in Phys.Rev.

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 N=1{\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