Developments of theory of effective prepotential from extended Seiberg–Witten system and matrix models - Itoyama, H.; Yoshioka, R. (Progress of theoretical and experimental physics, 2015)
This is a semi-pedagogical review of a medium size on the exact determination of and the role played by the low energy effective prepotential ${\mathcal {F}}$ in quantum field theory with (broken) extended supersymmetry, which began with the work of Seiberg and Witten in 1994. While paying attention to an overall view of the over two decades of development of this subject, we probe several corners marked in the three major stages of the developments, emphasizing uses of the deformation theory on the attendant Riemann surface as well as its close relation to matrix models. Examples picked here in different contexts tell us that the effective prepotential is to be identified as the suitably defined free energy $F$ of a matrix model: ${\mathcal {F}} = F$.