Narrow Results

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.

Making use of ansatzs for the form fields in the ten-dimensional type IIA supergravity version of the ABJM model, we come with a solution in the Euclidean signature recognized as a monopole instanton-like object. Indeed we will see that we can have a (anti-)self-dual solution at a special limit. While as a topological object, its backreaction on the original background should be ignorable, we show the energy–momentum tensors vanish exactly. On the field theory side, the best counterpart is an U(1) gauge field of a gauge transformation. To adjust with bulk, the gauge field must prompt to a dynamic one without adding any kinetic term for this dual photon except a marginal, Abelian AB-type Chern–Simons term on the boundary. We will see how both side solutions match next to another confirmation from some earlier works of this vortex–particle duality.