Curtain wall components for conserving dwelling heat by passive-solar means

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1983.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCHIncludes bibliographical references (p. 69-70).A prototype for a dwelling heat loss compensator is introduced in this thesis, along with its measured thermal performance and suggestions for its future development. As a heat loss compensator, the Sol-Clad-Siding collects, stores, and releases solar heat at room temperatures thereby maintaining a neutral skin for structures, which conserves energy, rather than attempting to supply heat into the interior as most solar systems do. Inhabitants' conventional objections to passive-solar systems utilized in housing are presented as a contrasting background. The potential of the outer component, a Trans-Lucent-Insulation as a sunlight diffuser and transmitter (65 to 52% of heating season insulation) and as a good insulator [0.62 W/(sq m) (°K) [0.11 Btu/(hr) (sq ft) (°F) 1] are described. The performance of the inner component, a container of phase-change materials as an efficient vertical thermal storage is discussed, and areas for future research are addressed. A very brief application of this passive-solar curtain wall system for dwellings is also given.by Doru Iliesiu.M.S

Monopole Operators in U(1)U(1) Chern-Simons-Matter Theories

We study monopole operators at the infrared fixed points of $U(1)$ Chern-Simons-matter theories (QED$_3$, scalar QED$_3$, ${\cal N} =1$ SQED$_3$, and ${\cal N} = 2$ SQED$_3$) with $N$ matter flavors and Chern-Simons level $k$. We work in the limit where both $N$ and $k$ are taken to be large with $\kappa = k/N$ fixed. In this limit, we extract information about the low-lying spectrum of monopole operators from evaluating the $S^2 \times S^1$ partition function in the sector where the $S^2$ is threaded by magnetic flux $4 \pi q$. At leading order in $N$, we find a large number of monopole operators with equal scaling dimensions and a wide range of spins and flavor symmetry irreducible representations. In two simple cases, we deduce how the degeneracy in the scaling dimensions is broken by the $1/N$ corrections. For QED$_3$ at $\kappa=0$, we provide conformal bootstrap evidence that this near-degeneracy is in fact maintained to small values of $N$. For ${\cal N} = 2$ SQED$_3$, we find that the lowest dimension monopole operator is generically non-BPS.Comment: 52 pages plus appendices, 9 figures, v2: minor correction

Bootstrapping O(N)O(N) Vector Models with Four Supercharges in 3≤d≤43 \leq d \leq4

We analyze the conformal bootstrap constraints in theories with four supercharges and a global $O(N) \times U(1)$ flavor symmetry in $3 \leq d \leq 4$ dimensions. In particular, we consider the 4-point function of $O(N)$-fundamental chiral operators $Z_i$ that have no chiral primary in the $O(N)$-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of $N+1$ chiral super-fields with superpotential $W = X \sum_{i=1}^N Z_i^2$, as well as general bounds on SCFTs where $\sum_{i=1}^N Z_i^2$ vanishes in the chiral ring.Comment: 25 pages, 8 figure

The Conformal Bootstrap at Finite Temperature

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical $O(N)$ model at leading order in $1/N$. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.Comment: 59 pages plus appendices, 14 figures. v2: added refs, minor correction

Bootstrapping 3D Fermions with Global Symmetries

We study the conformal bootstrap for 4-point functions of fermions $\langle \psi_i \psi_j \psi_k \psi_{\ell} \rangle$ in parity-preserving 3d CFTs, where $\psi_i$ transforms as a vector under an $O(N)$ global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the $O(N)$ symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the $1/N$ expansion at large $N$ and allow us to make nontrivial predictions at small $N$. For values of $N$ for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.Comment: 29 pages, 7 figure

Fermion-Scalar Conformal Blocks

We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called `seed blocks' in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.Comment: 25 pages; V2: added small clarifications to match JHEP versio

Bootstrapping 3D Fermions

We study the conformal bootstrap for a 4-point function of fermions $\langle\psi\psi\psi\psi\rangle$ in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the $\psi \times \psi$ OPE, and also on the central charge $C_T$. We observe features in our bounds that coincide with scaling dimensions in the Gross-Neveu models at large $N$. We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.Comment: 45 pages, 8 figures; V2: added references and small clarifications to match JHEP versio

Bootstrapping the 3d Ising model at finite temperature

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions 〈σσ〉 and 〈ϵϵ〉. As a result, we estimate the one-point functions of the lowest-dimension ℤ₂-even scalar ϵ and the stress energy tensor T_(μν). Our result for 〈σσ〉 at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE