BOOTSTRAP · Conformal Bootstrap Methods and their applications
FP7 — People (Marie Curie Actions)
- Duration
- 2014-09-01 → 2016-08-31
- EU contribution
- €207,929
- Participants
- 1
- Scheme
- MC-IEF
Lines connect the coordinator with its partners.
Results in brief
Conformal Bootstrap Methods and their applications
This project is concerned with the conformal bootstrap, a set of methods, mostly numerical, that are used to study conformal field theories. Such theories describe critical phenomena. The original plan for the scientific work is split into two parts. In the first part, “Applications and Theoretical development of the conformal bootstrap techniques”, we proposed to apply the methods of the conformal bootstrap to several cases of interest. One application was the study of supersymmetric conformal field theories. These are interesting both for theoretical as well as practical reasons. Theoretically supersymmetry gives us greater control over the theory which then allows for a precise comparison with numerical results. Practically, it is known that such theories have experimental applications as they can describe certain edge modes on the surface of topological insulators (Grover, Sheng, Vishawanath, Science 344), which makes them especially appealing to study. This work resulted in two publications in international peer-reviewed journals, described in section 3 of this note. In another application of the bootstrap methodology, the researcher studied the fractal Ising model. This is the critical theory underlying the Ising model on a fractal lattice. He has shown that if such a theory exists at all, then it must almost certainly be non-unitary. This surprising result was obtained by deriving bounds on conformal dimensions of operators for CFTs in several dimensions between one and two. This study resulted in a publication on the Journal of High Energy Physics. In other work, the author has developed the theory of logarithmic conformal field theories. Although such models had been studied to a large extent in two dimensions, their systematic description in higher dimensions is new. This serves as important preliminary work for future numerical bootstrap applications. Similar remarks apply to work done studying the long range Ising model, a model with a conformally invariant fixed point which should also be able to be tackled in future numerical studies. A surprising new application was to the study of the S-matrix. In what is perhaps one of the most exciting outcome of this project, the author has shown in collaboration with others that it is possible to obtain constraints on massive quantum field theories using methodology inspired by that of the conformal field theories. This resulted in two publications and more are forthcoming. The second part of this project was concerned with the development and publication of the numerical methods of the conformal bootstrap. This was achieved with the publication of the JuliBootS package (http://github.com/mfpaulos/JuliBoots/), the first publicly available package for bootstrap computations. The package was developed in the Julia programming language which allows for great flexibility combined with the speed and efficiency of Python and C. The package was accompanied by a bootstrap review which appeared in ([arXiv:1412.4127]). In what concerns the development of the numerical methods, the author has introduced the technique of extremal flows, which can improve numerical efficiency by several orders of magnitude. This technique introduces the notion of extremality of a spectrum to continuously deform approximate, numerical solutions to crossing symmetry. In many cases this is a vast improvement in current techniques.
Data: CORDIS, © European Union
Project objective
The conformal bootstrap methods are an exciting and fast-growing area of research, constituting a definite break-away from the more traditional (and often less rigorous) ways of studying systems at criticality. They provide us with a unique tool for exploring strongly coupled theories which are otherwise inaccessible, by using the powerful constraints of conformal symmetry. The European Union has an important opportunity in establishing itself now as a world leader in this promising, burgeoning field of research, by supporting projects such as the one we propose.We will study the O(N) vector models and their defects, examining their properties at criticality from the point of view of conformal symmetry. Our goal is to provide experimentalists and computational physicists with concrete testable predictions. We also hope to clarify any special analytic properties which may underlie these models. At the same time, we will develop the conformal bootstrap methodology, both theoretically and computationally. Finally, we will develop and publish a computer package for basic bootstrap calculations. This will allow for a greater number of researchers to use and adapt our techniques for their own purposes.The research project will take place at CERN, one of the world’s most active and perhaps largest research centers. The atmosphere is a vibrant one, with a department containing dozens of permanent researchers, fellows and a large number of temporary and long-term visitors. CERN is constituted by 20 member states, of which 18 belong to the EU, together with other four candidate or associate members. Such an international constitution guarantees a steady flow of ideas and many opportunities for cross-fertilization between fields, and international collaborations.
Original text from CORDIS.
Participants
- ORGANISATION EUROPEENNE POUR LA RECHERCHE NUCLEAIRE · GENEVE 23CoordinatorSwitzerland
Links
Data: CORDIS, © European Union