Multi-Instanton Measure from Recursion Relations in <i>N</i> = 2 Supersymmetric Yang-Mills Theory

Matone, Marco

doi:10.1088/1126-6708/2001/04/041

Cited by 9 publications

(16 citation statements)

References 25 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Before concluding, let us note that this approach should be related with the derivation of the structure of the instanton moduli space of N = 2 SYM obtained from the recursion relations for the instanton contributions to the prepotential [13]. In particular, it was shown how the analogs of the recursive structure of the Deligne-Knudsen-Mumford compactification of moduli space of Riemann surfaces and of the Wolpert restriction phenomenon, essentially determine the structure of the instanton moduli spaces.…”

Section: Restores Duality That Ismentioning

confidence: 99%

See 1 more Smart Citation

Seiberg–Witten duality in Dijkgraaf–Vafa theory

Matone¹

2003

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

We show that a suitable rescaling of the matrix model coupling constant makes manifest the duality group of the N = 2 SYM theory with gauge group SU (2). This is done by first identifying the possible modifications of the SYM moduli preserving the monodromy group. Then we show that in matrix models there is a simple rescaling of the pair (S D , S) which makes them dual variables with Γ(2) monodromy. We then show that, thanks to a crucial scaling property of the free energy derived perturbatively by Dijkgraaf, Gukov, Kazakov and Vafa, this redefinition corresponds to a rescaling of the free energy which in turn fixes the rescaling of the coupling constant. Next, we show that in terms of the rescaled free energy one obtains a nonperturbative relation which is the matrix model counterpart of the relation between the u-modulus and the prepotential of N = 2 SYM. This suggests considering a dual formulation of the matrix model in which the expansion of the prepotential in the strong coupling region, whose QFT derivation is still unknown, should follow from perturbation theory. The investigation concerns the SU (2) gauge group and can be generalized to higher rank groups.

show abstract

Section: Restores Duality That Ismentioning

confidence: 99%

“…These techniques are strictly related to the geometry of matrix models considered in the framework of Liouville quantum gravity [14]. So, it would be interesting to investigate whether there is a possible link between the matrix model approach to the N = 2 SYM and the geometrical approach considered in [13].…”

Section: Restores Duality That Ismentioning

confidence: 99%

Seiberg–Witten duality in Dijkgraaf–Vafa theory

Matone¹

2003

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

show abstract

“…The latter, together with the Wolpert restriction phenomenon, is at the heart of the recursion relations associated to the Painlevé I as derived in [25]. The analogy with the recursion relation for the N = 2 instantons suggested the formulation of instanton numbers in terms of intersection theory [26]. Recalling that 2D quantum gravity also leads to a natural triangulation of moduli space of Riemann surfaces, one might expect that a similar structure arises in instanton theory.…”

Section: Triangulating the Instanton Moduli Spacementioning

confidence: 96%

Branched matrix models and the scales of supersymmetric gauge theories

Matone

Mazzucato

2003

J. High Energy Phys.

Self Cite

View full text Add to dashboard Cite

In the framework of the matrix model/gauge theory correspondence, we consider supersymmetric U (N ) gauge theory with U (1) N symmetry breaking pattern. Due to the presence of the Veneziano-Yankielowicz effective superpotential, in order to satisfy the F -term condition i S i = 0, we are forced to introduce additional terms in the free energy of the corresponding matrix model with respect to the usual formulation. This leads to a matrix model formulation with a cubic potential which is free of parameters and displays a branched structure. In this way we naturally solve the usual problem of the identification between dimensionful and dimensionless quantities. Furthermore, we need not introduce the N = 1 scale by hand in the matrix model. These facts are related to remarkable coincidences which arise at the critical point and lead to a branched bare coupling constant.The latter plays the role of the N = 1 and N = 2 scales tuning parameter. We then show that a suitable rescaling leads to the correct identification of the N = 2 variables.Finally, by means of the mentioned coincidences, we provide a direct expression for the N = 2 prepotential, including the gravitational corrections, in terms of the free energy.This suggests that the matrix model provides a triangulation of the istanton moduli space.

show abstract

“…Recently in [1] it has been shown that the instanton moduli spaces of N = 2 Super Yang-Mills theory with gauge group SU(2) admit a compactification which is at the heart of the recursive relations derived in [2]. The structure of this compactification explains why, in spite of the technical difficulties, the Seiberg-Witten (SW) solution [3] is simple.…”

mentioning

confidence: 99%

“…Thus, essentially, the research started from the exact solution and ended with the reconstruction of the field theoretic structure of the theory. A basic point in [1] was the observation of the strict similarity between the properties of the instanton moduli space and its measure on the one hand and the corresponding quantities in the theory of punctured spheres, on the other. In particular, it has been shown that a compactification similar to the one by Deligne-Knudsen-Mumford [6] and the restriction phenomenon satisfied by the Weil-Petersson volume form [7] lead to the recursive structure obtained in the SW model.…”

mentioning

confidence: 99%

The instanton universal moduli space of N=2 supersymmetric Yang–Mills theory

Matone¹

2001

Physics Letters B

Self Cite

View full text Add to dashboard Cite

We use the recursive structure of the compactification of the instanton moduli space of N = 2 Super Yang-Mills theory with gauge group SU(2) to construct, by an inductive limit, a universal moduli space which includes all the multi-instanton moduli spaces. Furthermore, by exploiting an analogy with the strong and weak coupling expansions in the Matrix Model formulation of 2D Quantum Gravity, we discuss the possible field theoretical meaning of the contributions to the prepotential in the strong coupling region. In particular, whereas the weak and strong coupling expansions of the Painlevé I correspond to the genus and punctured spheres expansions, in the case of the instantons there should exist a space dual to the instanton moduli space.

show abstract

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

Abstract: By using the recursion relations found in the framework of N = 2 Super Yang-Mills theory with gauge group SU(2), we reconstruct the structure of the instanton moduli space and its volume form for all winding numbers.

Cited by 9 publications

References 25 publications

Seiberg–Witten duality in Dijkgraaf–Vafa theory

Seiberg–Witten duality in Dijkgraaf–Vafa theory

Branched matrix models and the scales of supersymmetric gauge theories

The instanton universal moduli space of N=2 supersymmetric Yang–Mills theory

Contact Info

Product

Resources

About