This is the foreword to the special volume on localization techniques in quantum field theory. The summary of individual chapters is given and their interrelation is discussed.

We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2, 0) superconformal theory on S 5 × S 1 . The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S 3 . With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N 3 scaling at large N . The large N index for U (N ) gauge group also completely agrees with the supergravity index on AdS 7 × S 4 .

Instanton partition functions of 5d N = 1 gauge theories are Witten indices for the ADHM gauged quantum mechanics with (0, 4) SUSY. We derive the integral contour prescriptions for these indices using the Jeffrey-Kirwan method, for gauge theories with hypermultiplets in various representations. The results can be used to study various 4d/5d/6d QFTs. In this paper, we study 5d SCFTs which are at the UV fixed points of 5d SYM theories. In particular, we focus on the Sp(N ) theories with N f ≤ 7 fundamental and 1 antisymmetric hypermultiplets, living on the D4-D8-O8 systems. Their superconformal indices calculated from instantons all show E N f +1 symmetry enhancements. We also discuss some aspects of the 6d SCFTs living on the M5-M9 system. It is crucial to understand the UV incompleteness of the 5d SYM, coming from small instantons in our problem. We explain in our examples how to fix them. As an aside, we derive the index for general gauged quantum mechanics with (0, 2) SUSY.

We construct consistent Kaluza-Klein reductions of D = 11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki-Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N = 2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki-Einstein space, and still consistent with N = 2 supersymmetry. In the context of flux compactifications, the Sasaki-Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G 2 manifold leading to an N = 1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N = 8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.

We study the index of N = 4 Yang-Mills theory on S 3 × R at large angular momenta. A generalized Cardy limit exhibits macroscopic entropy at large N . Our result is derived using free QFT analysis, and also a background field method on S 3 . The index sets a lower bound on the entropy. It saturates the Bekenstein-Hawking entropy of known supersymmetric AdS 5 black holes, thus accounting for their microstates. We further analyze the so-called Macdonald index, exploring small black holes and possibly new black holes reminiscent of hairy black holes. Finally, we study aspects of large supersymmetric AdS 7 black holes, using background field method on S 5 and 't Hooft anomalies.

Being inspired by gecko foot hairs, microfibers with flat spatulate tips are proposed as repeatable adhesives. They are fabricated by molding a master template fabricated using deep reactive ion etching and the notching effect. Fabricated polyurethane fiber arrays with 4.5μm fiber and 9μm tip diameter demonstrated macroscale adhesion pressures up to 18N∕cm2 and overall work of adhesion up to 11J∕m2 on a 6mm diameter glass hemisphere for a preload pressure of 12N∕cm2. These results show around four times higher adhesion and five times higher overall work of adhesion as compared to the flat polyurethane surface.

No abstract

Reversible control of adhesion is an important feature of many desired, existing, and potential systems, including climbing robots, medical tapes, and stamps for transfer printing. We present experimental and theoretical studies of pressure modulated adhesion between flat, stiff objects and elastomeric surfaces with sharp features of surface relief in optimized geometries. Here, the strength of nonspecific adhesion can be switched by more than three orders of magnitude, from strong to weak, in a reversible fashion. Implementing these concepts in advanced stamps for transfer printing enables versatile modes for deterministic assembly of solid materials in micro/nanostructured forms. Demonstrations in printed two- and three-dimensional collections of silicon platelets and membranes illustrate some capabilities. An unusual type of transistor that incorporates a printed gate electrode, an air gap dielectric, and an aligned array of single walled carbon nanotubes provides a device example.