A new derivation of the Picard-Fuchs equations for effective N = 2 super Yang-Mills theories

Isidro, J. M.; Mukherjee, Avijit; Nunes, João P.; Schnitzer, Howard J.

doi:10.1016/s0550-3213(97)00133-8

Cited by 32 publications

(35 citation statements)

References 34 publications

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“…When values of the mass parameters are generic, the analysis of the instanton correction is not as simple as that in the massless case. Already there exist much effort to obtain the prepotential in the massive case [8,9,10]. Rather than review these results, we will only remark on two points that will be of use later; on differential equations satisfied by (a, a D ) and on general structure of the prepotential.…”

Section: Massive Casementioning

confidence: 99%

Geometric engineering of Seiberg–Witten theories with massive hypermultiplets

Konishi

Naka

2003

Nuclear Physics B

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We analyze the geometric engineering of the N = 2 SU (2) gauge theories with 1 ≤ N f ≤ 3 massive hypermultiplets in the vector representation. The set of partial differential equations satisfied by the periods of the Seiberg-Witten differential is obtained from the Picard-Fuchs equations of the local B-model. The differential equations and its solutions are consistent with the massless case. We show that the Yukawa coupling of the local A-model gives rise to the correct instanton expansion in the gauge theory, and propose the pattern of the distribution of the world-sheet instanton number from it. As a side result, we obtain the asymptotic form of the instanton amplitude in the gauge theories with massless hypermultiplets.

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Section: Massive Casementioning

confidence: 99%

Geometric engineering of Seiberg–Witten theories with massive hypermultiplets

Konishi

Naka

2003

Nuclear Physics B

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“…17,18,19,20,21 Accordingly, collecting (2.7) for various k can generate a differential equation. In addition, since the all independent periods should be solutions to this equation, the order of the equation must coincide with the total number of them and in fact it is determined as 2n.…”

Section: B Derivation Of Picard-fuchs Odementioning

confidence: 99%

“…22,23,24 Similarly, for the SU(3) theory, we have 17) where the integration constant is normalized to 1 for convenience in the next section. Note that the regular singularities of (2.17) are the same with those of SU(3) Picard-Fuchs ODE.…”

Section: Wronskianmentioning

confidence: 99%

“…In these studies, general algorithms to get Picard-Fuchs equations were developed, 17,18,19,20,21 but these equations are in general realized as a set of simultaneous partial differential equations (PDEs) in terms of moduli derivatives. For this reason, it is not easy to solve Picard-Fuchs equations, especially, in higher rank gauge goup cases.…”

Section: Introductionmentioning

confidence: 99%

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

Ohta

1999

Journal of Mathematical Physics

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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)

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“…This linear relationship is the Picard-Fuchs equation. The procedure of constructing the one-forms on algebraic surfaces through differentiation with respect to the family parametre and discarding exact one-forms at each step has been used earlier in various contexts [10][11][12].…”

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confidence: 99%

An algebraic geometry method for calculating DOS for 2D tight binding models

Ray

Sen

2013

Advances in Theoretical and Mathematical Physics

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An algebraic geometry method is used to calculate the moments of the electron density of states as a function of the energy for lattices in the tight binding approximation. Interpreting the moments as the Mellin transform of the density allows writing down a formula for the density as an inverse Mellin transform. The method is illustrated by working out the density function for the two-dimensional square and honeycomb lattices.The tight binding model is a widely used scheme for studying electronic band structure of solids [1]. The model is defined by a Hamiltonian quadratic in the electron creation and destruction operators indexed by a set of points in the D-dimensional Euclidean space R D , called sites. The sites e-print archive: http://lanl.arXiv.org/abs/1205.1122

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A new derivation of the Picard-Fuchs equations for effective N = 2 super Yang-Mills theories

Cited by 32 publications

References 34 publications

Geometric engineering of Seiberg–Witten theories with massive hypermultiplets

Geometric engineering of Seiberg–Witten theories with massive hypermultiplets

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

An algebraic geometry method for calculating DOS for 2D tight binding models

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