HET seminar: Yuki Sato

Speaker: Yuki Sato

Title: Membrane interactions and a three-dimensional analog of Riemann surfaces

Abstract: 

I will discuss splitting interactions of membranes in M-theory based on the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. I will show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation. A description of configurations corresponding to membrane splitting processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of R³ connected via a generalisation of branch cuts. This talk will be based on the paper, JHEP 1602 (2016) 050, with Stefano Kovacs (Dublin IAS) and Hidehiko Shimada (KEK).