Multi-instanton calculus versus exact results in N = 2 supersymmetric QCD

Abstract

Microscopic tests of the exact results are performed in N = 2 supersymmetric SU (2) QCD. We present the complete construction of the multi-instanton in N = 2 supersymmetric QCD. All the defining equations of the super instanton are reduced to the algebraic equations. Using this result, we calculate the two-instanton contribution F 2 to the prepotential F for the arbitrary N f theories. For N f = 0, 1, 2, instanton calculus agrees with the prediction of the exact results, however, for N f = 3, 4, we find discrepancies between them. We propose improved curves of the exact results for the massive N f = 3 and massless N

On the uniqueness of the effective Lagrangian for N = 2 SQCD

“…Again this solution is identical to the solution proposed by Seiberg and Witten modulo the undetermined integration constant in the relation between u and z whose value can only be fixed by explicit 2-instanton computations [12]. For all the other candidates the Ward-identity does lead to extra constraints and the system is therefore over-determined.…”

“…Note that there is an ambiguity in the relation between u and z due to the integration constant u 0 . It is constrained to zero, either by an explicit 2-instanton computation [9,10,11,12] or by imposing invariance under the discrete R-transformations φ → e 2πi/3 φ [2].…”

“…Here we show that, in conjunction with the SL(2, Z)-structure, the superconformal anomaly determines the low-energy effective Lagrangian and completely parametrises the quantum moduli space. What distinguishes the 4-dimensional model is that the non-perturbative contributions are not computable by other means (except for 1 and 2 instantons contributions [8,9,10,11,12]). …”

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

“…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].…”

“…S G is the usual gauge field action, the kinetic terms for the Fermi and Bose fields minimally coupled to the gauge field A µ are 8) where λȦ are the two gauginos,Ȧ = 1, 2, and…”