Instantons and recursion relations in N = 2 SUSY gauge theory

Matone, Marco

doi:10.1016/0370-2693(95)00920-g

Cited by 304 publications

(324 citation statements)

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“…This achievement was possible thanks to a certain number of conjectures which were suggested by the physics of the problem. It was later shown in [3] that, in the case of N = 2 SYM, these assumptions follow from the symmetries of the theory and from the inversion formula first derived in [4] (subsequently generalised to SQCD in [5]), and are consistent with microscopic instanton computations in the cases of SYM and SQCD [6,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 64%

Nonholomorphic terms inN=2supersymmetric Wilsonian actions and the renormalization group equation

et al. 1997

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In this paper we first investigate the Ansatz of one of the present authors for K(Ψ,Ψ), the adimensional modular invariant non-holomorphic correction to the Wilsonian effective Lagrangian of an N = 2 globally supersymmetric gauge theory. The renormalisation group β-function of the theory crucially allows us to express K(Ψ,Ψ) in a form that easily generalises to the case in which the theory is coupled to N F hypermultiplets in the fundamental representation of the gauge group. This function satisfies an equation which should be viewed as a fully non-perturbative "non-chiral superconformal Ward identity". We also determine its renormalisation group equation. Furthermore, as a first step towards checking the validity of this Ansatz, we compute the contribution to K(Ψ,Ψ) from instantons of winding number k = 1 and k = 2. As a by-product of our analysis we check a non-renormalisation theorem for N F = 4.

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Section: Introductionmentioning

confidence: 64%

Nonholomorphic terms inN=2supersymmetric Wilsonian actions and the renormalization group equation

et al. 1997

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“…In the gauge theory formalism, this "quantum Matone relation" generalizes the classical Matone relation [87] with the inclusion of gravitational couplings [88][89][90][91][92], and it also has a natural interpretation in all-orders WKB [27,60,63]. At the classical level, → 0, the relation (1.5) is a simple consequence of the associated classical Picard-Fuchs equation, which characterizes the energy dependence of the classical action variables (see section 3.1.1 below).…”

Section: Jhep05(2017)087mentioning

confidence: 93%

“…The form of the Picard-Fuchs equation also leads to a natural definition of a classical prepotential [87]. To see this, simply invert the Picard-Fuchs equation (3.10) by writing the energy u as a function of the classical action a 0 :…”

Section: Jhep05(2017)087mentioning

confidence: 99%

Quantum geometry of resurgent perturbative/nonperturbative relations

Başar

Dunne

Ünsal

2017

J. High Energ. Phys.

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For a wide variety of quantum potentials, including the textbook 'instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and 'special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

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“…In particular, in the case of WP volumes one starts evaluating the recursion relations by means of the DeligneKnudsen-Mumford compactification and the Wolpert restriction phenomenon [17], then derives the associated nonlinear ODE [19] and end to a linear ODE [20] which is obtained by essentially inverting it. In the Seiberg-Witten model, one starts by observing that the a D (u) and a(u) moduli satisfy a linear ODE [21], inverts the equation to obtain a nonlinear one satisfied by u(a) then finds recursion relations for the coefficients of the expansion of u(a) [2]. The final point stems from the observation that u and F are related in a simple way which allows one to consider the derived recursion relation as a relation for the instanton contributions to the preportential F .…”

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confidence: 99%

Multi-Instanton Measure from Recursion Relations in N = 2 Supersymmetric Yang-Mills Theory

Matone

2001

J. High Energy Phys.

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Instantons and recursion relations in N = 2 SUSY gauge theory

Abstract: Finally, we find u = u(a) and give the explicit expression of F as function of u. These results can be extended to more general cases.

Cited by 304 publications

References 11 publications

Nonholomorphic terms inN=2supersymmetric Wilsonian actions and the renormalization group equation

Nonholomorphic terms inN=2supersymmetric Wilsonian actions and the renormalization group equation

Quantum geometry of resurgent perturbative/nonperturbative relations

Multi-Instanton Measure from Recursion Relations in N = 2 Supersymmetric Yang-Mills Theory

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