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Hyperkahler Sigma Model and Field Theory on Gibbons-Hawking Spaces

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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.

This talk is part of the Quantum Fields and Strings Seminars series.

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