The workshop on Exact Results in SUSY Gauge Theories in Various Dimensions took place from 11 to 22 August at CERN. It brought together leading experts in supersymmetric gauge theories from many universities and laboratories around the world to discuss recent progress on computing exact quantities in these theories. This event, organized by Boris Pioline and Wolfgang Lerche from CERN, Piljin Yi from the Korean Institute For Advanced Studies, and Seok Kim from the Seoul National University, is part of a series of Theory Institutes organized by the CERN Theory Unit on a regular basis.It was co-funded by the Korean government under the CERN-Korea collaboration.

The workshop covered recent advances in supersymmetric gaugetheories in various dimensions, which have become possible thanks to the development of localization techniques. These techniques allow to reduce the computation of certain supersymmetric observables to an integral over a finite number of degrees of freedom. The gauge theories of interest include matrix quantum mechanics, with applications to BPS bound states and wall-crossing phenomena, gauge linear sigma models in 2 dimensions and their implications to string theory and mirror symmetry, a large class of 3d/4d/5d gauge theories on a variety of curved spaces, and the enigmatic(2,0) superconformal theories in 6 dimensions. Some of the key observables are various manifestations of equivariant indices, partition functions on compact manifolds, and expectation values of extended supersymmetric operators.

The program consisted of two to three lectures per day, leaving ample time for discussions and collaboration.On Monday, the workshop began with two talks by Jaume Gomis and Cyril Closset on partition functions of supersymmetric field theories on curved spaces. On Tuesday, Kentaro Hori and Piljin Yi gave presentations on matrix quantum mechanics and wall crossing. The following days, speakers talked about quiver quantum mechanics (Jan Manschot), instanton partition functions (Stefano Cremonesi), quantum geometry (Marcos Marino Beiras and Hans Jockers) and five-dimensional gauge theories (Jaemo Park and Maxim Zabzine). In addition, Eric Sharpe, Kazuo Hosomichi, Sungjay Lee, Francesco Benini, and Abhijit Gadde focused on different aspects of two-dimensional gauge theories. VasilyPestun described in detail a correspondence between N=2 gauge theories and integrable systems. Zohar Komargodski gave a colloquium on “Emergent Gauge Symmetry”, and Sergey Gukov gave a general talk on geometry of 4-manifolds. The workshop concluded on Friday with Tomeu Fiol's presentation of the “Exact results for probes of Conformal Field Theories” and Silviu Pufu's talk on “The N=8 superconformal bootstrap in three dimensions”.

The indico page for this workshop can be found here.