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Math-Physics Joint Seminar

Tuesday, October 16, 2018 - 4:30pm

Pietro Antonio Grassi

Deputy Director, Arnold-Regge Center, Univ. del Piemonte Orientale


University of Pennsylvania


Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms “extend” the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like. Applications to physics is also illustrated.