Trivial and Non-trivial Defect Conformal Manifolds

It has been known for many years that there exist families of superconformal field theories (SCFTs) connected by exactly marginal deformations. Such families are called “conformal manifolds”. In the presence of boundaries or defects, we can study the analogue construction, defect conformal manifolds. Just as exactly marginal operators parameterise the conformal manifold, the corresponding operators on conformal defects allow for their marginal deformations.In this thesis, we consider two kinds of defect exactly marginal operators. One is “trivial” that arises from global symmetry breaking. When a defect breaks a global symmetry, there is a contact term in the conservation equation with defect exactly marginal operators. The resulting defect conformal manifold is the symmetry breaking coset and its Zamolodchikov metric is expressed as the 2-point function of the exactly marginal operators. As the Riemann tensor on the conformal manifold can be expressed as an integrated 4-point function of the marginal operators, we find an exact relation to the curvature of the coset space. We confirm this relation against previously obtained 4-point functions for insertions into the 1/2 BPS Wilson loop in N = 4 super Yang Mills, the 1/2 BPS surface operator of the 6d N = (2, 0) theory and 1/2 BPS Wilson loops in ABJM theory. We also construct the 1/3 BPS loops in ABJM and examine the relation there.However, defect conformal manifolds do not require broken symmetries. One natural setting is in 3d, where line operators have multiple marginal couplings. We constructed many new moduli spaces of both conformal and non-conformal BPS Wilson loops in N = 4 quiver Chern-Simons-matter theory on S3, connected by continuous supersymmetric deformations. In the case of conformal BPS loops, the deformations play the role of defect exactly marginal operators which generate the “nontrivial” conformal manifolds. With the same method, we also address a longstanding question of whether ABJM theory has 1/3 BPS Wilson loop operators, where such loops are made of a large supermatrix combining two 1/2 BPS Wilson loops.<br/

1/3 BPS loops and defect CFTs in ABJM theory

We address a longstanding question of whether ABJM theory has Wilson loop operators preserving eight supercharges (so 1/3 BPS). We present such Wilson loops made of a large supermatrix combining two 1/2 BPS Wilson loops. We study the spectrum of operator insertions into them including the displacement operator and several others and study their correlation functions. Another natural construction arising in this context are Wilson loops with alternating superconnections. This amounts to including "defect changing operators" along the loop, similar to a discrete cusp. This insertion is topological and preserves two supercharges. We study the multiplet of this operator and how it can be used to introduce further operators. We also construct the defect conformal manifold arising from marginal defect operators.Comment: 38 pages, half of them appendices; V2: minor changes, version to appear in JHE

The planar limit of integrated 4-point functions

We compute the planar limit, as all-order power series in the 't Hooft coupling, of various integrated 4-point functions of chiral primary operators of ${\cal N}=4$ SU(N) super Yang-Mills, and of moment map operators of ${\cal N}=2$ SU(N) SQCD. We do so by computing the planar free energy on $S^4$ of the respective massive deformations of these theories, and then taking advantage of the exact relation between these free energies and the integrated 4-point functions.Comment: 23 page

Classifying BPS bosonic Wilson loops in 3d N=4 Chern-Simons-matter theories

We study the possible BPS Wilson loops in three-dimensional N = 4 Chern-Simons-matter theory which involve only the gauge field and bilinears of the scalars. Previously known examples are the analogues of the Gaiotto-Yin loops preserving four supercharges and “latitude” loops preserving two. We carry out a careful classification and find, in addition, loops preserving three supercharges, further inequivalent classes of loops preserving two supercharges and loops preserving a single supercharge. For each of the classes of loops, we present a representative example and analyse their full orbit under the broken symmetries

Broken R-symmetry and defect conformal manifolds

Just as exactly marginal operators allow to deform a conformal field theory along the space of theories known as the conformal manifold, appropriate operators on conformal defects allow for deformations of the defects. A setup that guarantees exactly marginal defect operators in theories with extended supersymmetry are defects that break the R-symmetry group. In that case the conformal manifold is the symmetry breaking coset and its Zamolodchikov metric is expressed as the two point function of the exactly marginal operator. As the Riemann tensor on the conformal manifold can be expressed as an integrated correlator of the marginal operators, we find an exact relation to the curvature of the coset space.We examine in detail the case of the 1/2 BPS Maldacena-Wilson loop in $\mathcal{N}=4$ SYM, which breaks $SO(6)\to SO(5)$ and the 1/2 BPS surface operator of the 6d $\mathcal{N}=(2,0)$ theory with $SO(5)\to SO(4)$ breaking. We verify this identity against known 4-point functions, previously derived from AdS/CFT and the conformal bootstrap.Comment: 19 page

A network of hyperloops

Abstract In this paper we complete the exploration of connected components of the space of BPS Wilson loops in three-dimensional N $$\mathcal{N}$$ = 4 Chern-Simons-matter theory on S 3. The algorithm is to start with a supersymmetric Wilson loop, choose a preserved supercharge, and look for BPS deformations built out of the matter fields in the proper representations. Using this, we discover many new moduli spaces of nonconformal BPS Wilson loops preserving a single or two supercharges, which are subsets of the symmetries of the 1/4 and 3/8 BPS operators. Along with the those previously found in [1, 2] and [3], the total moduli spaces are closed under this formalism

1/3 BPS loops and defect CFTs in ABJM theory

Abstract We address a longstanding question of whether ABJM theory has Wilson loop operators preserving eight supercharges (so 1/3 BPS). We present such Wilson loops made of a large supermatrix combining two 1/2 BPS Wilson loops. We study the spectrum of operator insertions into them including the displacement operator and several others and study their correlation functions. Another natural construction arising in this context are Wilson loops with alternating superconnections. This amounts to including “defect changing operators” along the loop, similar to a discrete cusp. This insertion is topological and preserves two supercharges. We study the multiplet of this operator and how it can be used to introduce further operators. We also construct the defect conformal manifold arising from marginal defect operators

Thermal insulating properties of hollow mullite fibers prepared on a ceiba bio-template

Ceiba fibers have excellent thermal insulating properties because of their hollow structures. Mullite fibers are widely used in heat-insulating refractory materials because of their low thermal conductivity and excellent thermal shock stability. However, unlike ceiba fibers, conventional mullite fibers have solid structures, which limits further development of the thermal insulating properties of mullite fibers. Inspired by their hollow structure, we used ceiba fibers as a template for preparing hollow mullite fibers. We immersed ceiba fibers in a precursor solution of Al(NO3)3 and ethyl orthosilicate (TEOS). The impregnated ceiba fibers were then dried and sintered at a high temperature to obtain hollow mullite fibers. The synthesis process, microstructures, phases, pore size distributions, and thermal conductivities of the resulting fibers were analyzed. The results showed that mullite fibers inherited the hollow structure of the ceiba fibers, and the resulting thermal conductivity was markedly reduced compared to solid mullite fibers

Flow shop scheduling of hybrid make-to-stock and make-to-order in a distributed precast concrete production system

Prefabrication is not only economically optimal but also environmentally sustainable; hence, it is the future of construction. Furthermore, mass customization is the future of prefabrication. In the mass customization era, the production paradigm in precast concrete (PC) factories will inevitably shift toward a blend of make-to-order (MTO) and make-to-stock (MTS) from the current MTO dominant model. Because PC factories have more motivation to fulfill MTO orders to secure profit, a hierarchical scheduling mechanism of MTO first and MTS second seems reasonable. Meanwhile, an emerging trend of expanding factories overseas is observed in the PC industry, especially in land-scarce countries like Singapore. Given additional resources, the new multiple-factory production network leads to relatively relaxed MTO due dates, which makes the proposed hierarchical scheduling mechanism more sensible. However, finding an optimal production plan for hybrid MTO and MTS on multiple production lines is not easy. There is an assignment problem in addition to the scheduling problem. Both the assignment problem and the scheduling problem are in the class of combinatorial optimization problems (COPs). Given that the use of meta-heuristics for solving complex COPs is a rapidly growing research topic, this paper employs meta-heuristic methods to solve the two problems simultaneously. Comparisons between the genetic algorithm and the whale optimization algorithm are made. Through the computational evaluation of a test case, the performance and effectiveness of the proposed methods are verified.Published versio