The structure of the gauge group constrains the properties of operators in a gauge theory. In this talk, I will consider the reverse direction and ask what properties of a (finite) gauge group can be reconstructed from the operators in a gauge theory. I will first consider OPE/fusion rules of Wilson lines, and explain various properties of the gauge group that can be deduced from it. Then I will introduce certain surface operators which exist in any gauge theory. I will describe the fusion rules of these surface operators, and show that, in general, there are properties of the gauge group that can be reconstructed from the fusion rules of surface operators which cannot be obtained from the fusion rules of Wilson lines, and vice-versa.
This talk is based on arXiv:2302.08419.
Zoom link: https://icts-res-in.zoom.us/j/82749996971?pwd=enVyZlJOTEhkZ1U3NEpDRnMwVDQ4dz09
Meeting ID: 827 4999 6971
Passcode: 303031