This is a two week long Theory Institute at CERN devoted to recent developments in M-theory. In 2012, a 6 month long programme on this topic was organised at the Isaac Newton Institute in Cambridge, UK entitled Mathematics and Applications of Branes in String and M-theory. Since the meeting was very successful, helping to stimulate a variety of subsequent developments. One-week long follow-up meetings were held in Banff, Canada (Modern Developments in M-theory, January 2014) and Gangwondo, Korea (2nd Workshop on Developments in M-theory, January 2015). The field has continued to develop, while several important challenges remain to be addressed. We thus organise a two week meeting from February 8 to February 19 2016, after the CERN Winter School.

In particular we have identified the following themes that are current of interest:

1 Localization calculations of superconformal indices in 5 and 6 dimensions and higher dimensional gauge theories

Recent work has shown that exact results can be computed in superconformal field theories using localization techniques. This opens up a new possibility to explore strongly coupled field theories in higher dimensions. On a related note there has also been significant progress in understanding the appearance of enhanced flavour and Lorentz symmetries in five dimensional theories using, for example, five-dimensional analogues of monopole operators known as instanton operators.

2 The bootstrap approach to conformal field theories

There has recently been a revival of bootstrap techniques for conformal field theories above two dimensions. The new techniques primarily rely on numerical techniques to place bounds, sometimes quite precise, on the dimensions of operators. These techniques do not rely on having small perturbation parameters. Indeed they work best for theories with no continuous parameters and hence the there has been recent interesting work on applying them to the (2,0) theory.

3 Field theory models of M-branes, in particular M5-branes

Although the M2-branes of M-theory are now relatively well understood the M5-brane (described by the (2,0) theory) remains an enigma. Complimentary to formal work done to understand the (2, 0) theory is the development of field theory models that can capture the physics of M5-branes and help elucidate its relationship to gauge theories. It would also be of interest to revisit some of the structure of M-theory implied by the M2-brane models without taking a large N limit.

4 Higher spin gravity

The generalisation of quantum gravity to incorporate gauge fields of higher spin has gained attention in recent years and led to new insights into the AdS/CFT correspondence. In four-dimensions the higher spin theories can related to duals of ABJ models of M2-branes.

The structure of the Theory Institute includes a small number of talks each day, typically around 3 or 4, with plenty of time scheduled for discussions and interactions.

This Theory Institute is also supported by the CERN-Korea program.

Organizers: Neil Lambert, Kimyeong Lee, Noppadol Mekareeya, Sunil Mukhi and Piljin Yi