Dynamical Dark Matter from Strongly-Coupled Dark Sectors

Dynamical Dark Matter (DDM) is an alternative framework for dark-matter physics in which the dark sector comprises a vast ensemble of particle species whose decay widths are balanced against their cosmological abundances. Previous studies of this framework have focused on a particular class of DDM ensembles --- motivated primarily by KK towers in theories with extra dimensions --- in which the density of states scales roughly as a polynomial of mass. In this paper, by contrast, we study the properties of a different class of DDM ensembles in which the density of states grows exponentially with mass. Ensembles with this Hagedorn-like property arise naturally as the "hadrons" associated with the confining phase of a strongly-coupled dark sector; they also arise naturally as the gauge-neutral bulk states of Type I string theories. We study the dynamical properties of such ensembles, and demonstrate that an appropriate DDM-like balancing between decay widths and abundances can emerge naturally --- even with an exponentially rising density of states. We also study the effective equations of state for such ensembles, and investigate some of the model-independent observational constraints on such ensembles that follow directly from these equations of state. In general, we find that such constraints tend to introduce correlations between various properties of these DDM ensembles such as their associated mass scales, lifetimes, and abundance distributions. For example, we find that these constraints allow DDM ensembles with energy scales ranging from the GeV scale all the way to the Planck scale, but the total present-day cosmological abundance of the dark sector must be spread across an increasing number of different states in the ensemble as these energy scales are dialed from the Planck scale down to the GeV scale. Numerous other correlations and constraints are also discussed.Comment: 29 pages, LaTeX, 10 figure

Critical Sp(N)Sp(N) Models in 6−ϵ6-\epsilon Dimensions and Higher Spin dS/CFT

Theories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field Theory correspondence. We consider an $Sp(N)$ invariant theory of $N$ anti-commuting scalars and one commuting scalar, which has cubic interactions and is renormalizable in 6 dimensions. For any even $N$ we find an IR stable fixed point in $6-\epsilon$ dimensions at imaginary values of coupling constants. Using calculations up to three loop order, we develop $\epsilon$ expansions for several operator dimensions and for the sphere free energy $F$. The conjectured $F$-theorem is obeyed in spite of the non-unitarity of the theory. The $1/N$ expansion in the $Sp(N)$ theory is related to that in the corresponding $O(N)$ symmetric theory by the change of sign of $N$. Our results point to the existence of interacting non-unitary 5-dimensional CFTs with $Sp(N)$ symmetry, where operator dimensions are real. We conjecture that these CFTs are dual to the minimal higher spin theory in 6-dimensional de Sitter space with Neumann future boundary conditions on the scalar field. For $N=2$ we show that the IR fixed point possesses an enhanced global symmetry given by the supergroup $OSp(1|2)$. This suggests the existence of $OSp(1|2)$ symmetric CFTs in dimensions smaller than 6. We show that the $6-\epsilon$ expansions of the scaling dimensions and sphere free energy in our $OSp(1|2)$ model are the same as in the $q \rightarrow 0$ limit of the $q$-state Potts model.Comment: 16 pages, 3 figures. v3: added relation to the q=0 Potts model. Some improvements and references adde

Generalized FF-Theorem and the ϵ\epsilon Expansion

Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient $a$ of the Weyl anomaly, while in odd dimensions to the sphere free energy $F$. In recent work arXiv:1409.1937 it was suggested that the $a$- and $F$-theorems may be viewed as special cases of a Generalized $F$-Theorem valid in continuous dimension. This conjecture states that, for any RG flow from one conformal fixed point to another, $\tilde F_{\rm UV} > \tilde F_{\rm IR}$, where $\tilde F=\sin (\pi d/2)\log Z_{S^d}$. Here we provide additional evidence in favor of the Generalized $F$-Theorem. We show that it holds in conformal perturbation theory, i.e. for RG flows produced by weakly relevant operators. We also study a specific example of the Wilson-Fisher $O(N)$ model and define this CFT on the sphere $S^{4-\epsilon}$, paying careful attention to the beta functions for the coefficients of curvature terms. This allows us to develop the $\epsilon$ expansion of $\tilde F$ up to order $\epsilon^5$. Pade extrapolation of this series to $d=3$ gives results that are around $2-3\%$ below the free field values for small $N$. We also study RG flows which include an anisotropic perturbation breaking the $O(N)$ symmetry; we again find that the results are consistent with $\tilde F_{\rm UV} > \tilde F_{\rm IR}$.Comment: 41 pages, 7 figures. v3: minor improvement

On CJC_J and CTC_T in the Gross-Neveu and O(N)O(N) Models

We apply large $N$ diagrammatic techniques for theories with double-trace interactions to the leading corrections to $C_J$, the coefficient of a conserved current two-point function, and $C_T$, the coefficient of the stress-energy tensor two-point function. We study in detail two famous conformal field theories in continuous dimensions, the scalar $O(N)$ model and the Gross-Neveu model. For the $O(N)$ model, where the answers for the leading large $N$ corrections to $C_J$ and $C_T$ were derived long ago using analytic bootstrap, we show that the diagrammatic approach reproduces them correctly. We also carry out a new perturbative test of these results using the $O(N)$ symmetric cubic scalar theory in $6-\epsilon$ dimensions. We go on to apply the diagrammatic method to the Gross-Neveu model, finding explicit formulae for the leading corrections to $C_J$ and $C_T$ as a function of dimension. We check these large $N$ results using regular perturbation theory for the Gross-Neveu model in $2+\epsilon$ dimensions and the Gross-Neveu-Yukawa model in $4-\epsilon$ dimensions. For small values of $N$, we use Pade approximants based on the $4-\epsilon$ and $2+\epsilon$ expansions to estimate the values of $C_J$ and $C_T$ in $d=3$. For the $O(N)$ model our estimates are close to those found using the conformal bootstrap. For the GN model, our estimates suggest that, even when $N$ is small, $C_T$ differs by no more than $2\%$ from that in the theory of free fermions. We find that the inequality $C_T^{\textrm{UV}} > C_T^{\textrm{IR}}$ applies both to the GN and the scalar $O(N)$ models in $d=3$.Comment: 62 pages, 34 figures. v2: minor improvements, references adde

BRST Structures and Symplectic Geometry on a Class of Supermanifolds

By investigating the symplectic geometry and geometric quantization on a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed and q-deformed cases in the classical as well as in the quantum cases.Comment: 14 pages, Late