# Topological quantum mechanics and Higgs branches of 3d N=4 theories

### APA

Dedushenko, M. (2016). Topological quantum mechanics and Higgs branches of 3d N=4 theories. Perimeter Institute. https://pirsa.org/16120005

### MLA

Dedushenko, Mykola. Topological quantum mechanics and Higgs branches of 3d N=4 theories. Perimeter Institute, Dec. 06, 2016, https://pirsa.org/16120005

### BibTex

@misc{ pirsa_PIRSA:16120005, doi = {10.48660/16120005}, url = {https://pirsa.org/16120005}, author = {Dedushenko, Mykola}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Topological quantum mechanics and Higgs branches of 3d N=4 theories}, publisher = {Perimeter Institute}, year = {2016}, month = {dec}, note = {PIRSA:16120005 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

3d N=4 theories on the sphere have interesting supersymmetric sectors described by 1d QFTs and defined as the cohomology of a certain supercharge. One can define such a 1d sector for the Higgs branch or for the Coulomb branch. We study the Higgs branch case, meaning that the 1d QFT captures exact correlation functions of the Higgs branch operators of the 3d theory. The OPE of the 1d theory gives a star-product on the Higgs branch which encodes the data of these correlation functions. When the 3d theory is superconformal, the 1d theory is topological and coincides with the known construction in flat space, where the topological 1d theory lives in the cohomology of Q+S. Our construction thus generalizes it away from the conformal point. We then focus on theories constructed from vector and hypermultiplets. Using supersymmetric localization, we explicitly describe their 1d sector as the gauged topological quantum mechanics, or equivalently a gaussian theory coupled to a matrix model. This provides a very simple technique to compute the Higgs branch correlators.