AdS4_4/CFT3_3 for Unprotected Operators

We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in $\mathcal{N}=8$ ABJ(M) theory \cite{Aharony:2008ug, Aharony:2008gk}. At large central charge $c_T\sim N^{3/2}$, this correlator is given by the corresponding holographic correlation function in 11d supergravity on $AdS_4\times S^7$. We use Mellin space techniques to compute the leading $1/c_T$ correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator. For half and quarter-BPS operators, we find exact agreement with previously computed localization results. For the other BPS and non-BPS operators, our results match the $\mathcal{N}=8$ numerical bootstrap for ABJ(M) at large $c_T$, which provides a precise check of unprotected observables in AdS/CFT.Comment: 22 pages, 1 figure, v4, fixed typo

A comparison of the physical and chemical composition of UK waste streams based on hypothetical compound structure

The suitability and effectiveness of a waste treatment process or strategy depends upon a waste stream’s physical and chemical composition. Chemical properties of UK waste streams, particularly MSW, are limited while physical properties are better documented. Consequently this presents a degree of uncertainty with the waste’s properties, manifesting itself as financial risk in the investment of new treatment or disposal plant. To mitigate this uncertainty, a number of UK waste surveys have been reviewed to determine if there is significant difference in the calorific value between waste streams. Ultimate and proximate analysis data from a number of sources have been collected and used to approximate the chemical composition of each waste fraction. To facilitate the comparison of each waste stream, a hypothetical compound of the form C6HaOb has been determined for each. Based on this analysis, all UK waste streams share the hypothetical formula C6H10O3, indicating that on a dry basis, the composition of waste in the UK is fairly consistent. Monte Carlo analysis of the hypothetical compound structure revealed that for both household and civic amenity waste streams, the hydrogen and oxygen content only deviate slightly from the mean values. Since MSW is predominantly comprised of household and civic amenity waste, the hypothetical compound C6H10O3 can be used to approximate UK MSW

M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture

We study various aspects of the M-theory uplift of the $A_{N-1}$ series of $(2,0)$ CFTs in 6d, which describe the worldvolume theory of $N$ M5 branes in flat space. We show how knowledge of OPE coefficients and scaling dimensions for this CFT can be directly translated into features of the momentum expansion of M-theory. In particular, we develop the expansion of the four-graviton S-matrix in M-theory via the flat space limit of four-point Mellin amplitudes. This includes correctly reproducing the known contribution of the $R^4$ term from 6d CFT data. Central to the calculation are the OPE coefficients for half-BPS operators not in the stress tensor multiplet, which we obtain for finite $N$ via the previously conjectured relation [arXiv:1404.1079] between the quantum ${\cal W}_N$ algebra and the $A_{N-1}$ $(2,0)$ CFT. We further explain how the $1/N$ expansion of ${\cal W}_N$ structure constants exhibits the structure of protected vertices in the M-theory action. Conversely, our results provide strong evidence for the chiral algebra conjecture.Comment: 30+18 pages. v2: added refs, fixed typos/notatio

Towards Bootstrapping QED3_3

We initiate the conformal bootstrap study of Quantum Electrodynamics in $2+1$ space-time dimensions (QED$_{3}$) with $N$ flavors of charged fermions by focusing on the 4-point function of four monopole operators with the lowest unit of topological charge. We obtain upper bounds on the scaling dimension of the doubly-charged monopole operator, with and without assuming other gaps in the operator spectrum. Intriguingly, we find a (gap-dependent) kink in these bounds that comes reasonably close to the large $N$ extrapolation of the scaling dimensions of the singly-charged and doubly-charged monopole operators down to $N=4$ and $N=6$.Comment: 29 pages plus an appendix, 5 figures, v2 minor improvements, refs adde

Urban heat stress vulnerability in the U.S. Southwest: The role of sociotechnical systems

Heat vulnerability of urban populations is becoming a major issue of concern with climate change, particularly in the cities of the Southwest United States. In this article we discuss the importance of understanding coupled social and technical systems, how they constitute one another, and how they form the conditions and circumstances in which people experience heat. We discuss the particular situation of Los Angeles and Maricopa Counties, their urban form and the electric grid. We show how vulnerable populations are created by virtue of the age and construction of buildings, the morphology of roads and distribution of buildings on the landscape. Further, the regulatory infrastructure of electricity generation and distribution also contributes to creating differential vulnerability. We contribute to a better understanding of the importance of sociotechnical systems. Social infrastructure includes codes, conventions, rules and regulations; technical systems are the hard systems of pipes, wires, buildings, roads, and power plants. These interact to create lock-in that is an obstacle to addressing issues such as urban heat stress in a novel and equitable manner

Bootstrapping O(N)O(N) Vector Models in 4<d<64<d<6

We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $\phi_i$ transforming as an $O(N)$ vector. The crossing symmetry of the four-point function of this $O(N)$ vector operator, along with unitarity assumptions, determine constraints on the scaling dimensions of conformal primary operators in the $\phi_i \times \phi_j$ OPE. Imposing a lower bound on the second smallest scaling dimension of such an $O(N)$-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting $O(N)$-symmetric CFT conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest $O(N)$ singlet in the $\phi_i \times \phi_j$ OPE, we observe that this kink disappears in $d =5$ for small enough $N$, suggesting that in this case an interacting $O(N)$ CFT may cease to exist for $N$ below a certain critical value.Comment: 24 pages, 5 figures; v2 minor improvement

Heat pipe cooling of power processing magnetics

A heat pipe cooled transformer and input filter were developed for the 2.4 kW beam supply of a 30 cm ion thruster system. This development yielded a mass reduction of 40% (1.76 kg) and lower mean winding temperature (20 C lower). While these improvements are significant, preliminary designs predict even greater benefits to be realized at higher power. The design details are presented along with the results of thermal vacuum operation and the component performance in a 3 kW breadboard power processor

Solving M-theory with the Conformal Bootstrap

We use the conformal bootstrap to perform a precision study of 3d maximally supersymmetric ($\mathcal{N}=8$) SCFTs that describe the IR physics on $N$ coincident M2-branes placed either in flat space or at a \C^4/\Z_2 singularity. First, using the explicit Lagrangians of ABJ(M) \cite{Aharony:2008ug,Aharony:2008gk} and recent supersymmetric localization results, we calculate certain half and quarter-BPS OPE coefficients, both exactly at small $N$, and approximately in a large $N$ expansion that we perform to all orders in $1/N$. Comparing these values with the numerical bootstrap bounds leads us to conjecture that some of these theories obey an OPE coefficient minimization principle. We then use this conjecture as well as the extremal functional method to reconstruct the first few low-lying scaling dimensions and OPE coefficients for both protected and unprotected multiplets that appear in the OPE of two stress tensor multiplets for all values of $N$. We also calculate the half and quarter-BPS operator OPE coefficients in the $SU(2)_k \times SU(2)_{-k}$ BLG theory for all values of the Chern-Simons coupling $k$, and show that generically they do not obey the same OPE coefficient minimization principle.Comment: 30 pages, 5 figures, v2 submitted for publicatio

A New Duality Between N=8\mathcal{N}=8 Superconformal Field Theories in Three Dimensions

We propose a new duality between two 3d $\mathcal{N}=8$ superconformal Chern-Simons-matter theories: the $U(3)_1 \times U(3)_{-1}$ ABJM theory and a theory consisting of the product between the $\left(SU(2)_3\times SU(2)_{-3}\right)/\mathbb{Z}_2$ BLG theory and a free ${\cal N} = 8$ theory of eight real scalars and eight Majorana fermions. As evidence supporting this duality, we show that the moduli spaces, superconformal indices, $S^3$ partition functions, and certain OPE coefficients of BPS operators in the two theories agree.Comment: 29 pages, 2 figure