Instanton Corrections to Hypermultiplet Moduli Spaces

          @misc{ scivideos_PIRSA:12020139,
            doi = {10.48660/12020139},
            url = {https://pirsa.org/12020139},
            author = {Saueressig, Frank},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Instanton Corrections to Hypermultiplet Moduli Spaces},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2012},
            month = {feb},
            note = {PIRSA:12020139 see, \url{https://scivideos.org/index.php/pirsa/12020139}}
          }
          

Abstract

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is still an open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.