New methods to count instantons
이기홍 · Seoul National University Open Repository (Seoul National University) · 2020
In this thesis we introduce new methods to count instantons in 4,5 and 6 dimensions.When the gauge group is classical simple Lie group, instanton moduli space can be understood by ADHM formalism which are a matrix theory with auxiliary(gauge) group and its 1d or 2d gauged extension on the worldline/sheet of an instanton particle(5d)/string(6d).However there are difficulties in understanding instanton moduli by the lack of known ADHM construction when the gauge group is exceptional or matters are in exotic representations.Among such cases, one may compute instanton partition functions by extending ADHM formalism of classical gauge group.With this method we also compute partition function of self-dual strings in 6d N = (1, 0) non-Higgsable cluster SCFTs.On the other hand one can obtain the so-called "blowup equation" which is the consistency condition that the partition function satisfies by blowing-up the center of instanton in R 4 .Using blowup equations, one can recursively compute the instanton partition function for general gauge group and matters by knowing the perturbative partition function.In the later part of the thesis we first derive the blowup equations of 4d N = 2 partition functions, find analogous blowup equations in 5d, surveying when they satisfy, and finaly compute the instanton partition functions of general gauge group and matters using them.