# Hyperkahler Sigma Model and Field Theory on Gibbons-Hawking Spaces

19 May 2014
12:00
Abstract
<em> We will introduce a deformed version of the 3d hyperkahler sigma model which arises from the compactification of d=4,N=2 gauge theories on a Gibbons-Hawking space. After discussing extensions of the relevant hyperkahler identities from the standard story, we will derive the condition for which the deformed sigma model preserves 4 out of the 8 supercharges. Using supersymmetry considerations, we will also demonstrate that the contribution of the NUT center to the sigma model path integral is a holomorphic section of a certain holomorphic line bundle over the hyperkahler target. As a concrete example, we will discuss the case where the original 4d theory is a U(1) super Yang-Mills and show that the NUT center contribution in this case is the Jacobi theta function.</em>
• String Theory Seminar