Picard–Fuchs ordinary differential systems in N=2 supersymmetric Yang–Mills theories

Abstract

In general, Picard-Fuchs systems in N = 2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard-Fuchs ODEs. In contrast with the usual Picard-Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli and QCD scale parameter, which in the case of SU (2)

Exact Results for Topological Strings on Resolved Y p,q Singularities

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Instanton correction of prepotential in Ruijsenaars model associated with N=2 SU(2) Seiberg–Witten theory

“…The effective action of gauge theory occasionally including massive hypermultiplets in the fundamental representation of the gauge group has been discussed in many view points, and accordingly, we have now much acquaintance with various properties of the prepotential and it's related materials, such as Picard-Fuchs equations for periods, 3,4,5,6,7 renormalization group like equation for prepotential, 8,9,10,11,12,13 relation to integrable systems, 14,15 appearance of WDVV equations, 16,17,18 flat coordinates 19,20 and so on.…”

Picard–Fuchs equations and Whitham hierarchy in N=2 supersymmetric SU(r+1) Yang–Mills theory

“…It is interesting that the instanton contributions to prepotential 17 can be obtained from the evaluation of periods and the prepotentials obtained in this way 18,19,20,21,22,23,24,25,26 are known to be consistent to the instanton calculus. 26,27,28,29,30,31,32,33 In these studies, the method based on Picard-Fuchs equations 18,19,20,21,22,23,24,25,34,35,36,37,38 played a crucial role.…”