Testing Seiberg-Witten Solution

2000

In this letter we argue that instanton–dominated Green’s functions in N = 2 Super Yang–Mills theories can be equivalently computed either using the so–called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg–Witten effective action for the low–energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self–dual gauge connections. 1

Physics Letters B, 2000

In this letter we argue that instanton-dominated Green's functions in N = 2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg-Witten effective action for the low-energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self-dual gauge connections.

2000

The results obtained by Seiberg and Witten for the low–energy Wilsonian effective actions of N = 2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non–perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N = 2 Super Yang–Mills theory. After extending the standard construction of the Topological Yang–Mills theory to encompass the case of a non–vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so–called “constrained instanton ” configurations and the instanton measure arise in a natural way. As a consequence, insta...

Exact solutions to the low-energy effective action (LEEA) of the four-dimensional (4d), N = 2 supersymmetric gauge theories with matter (including N = 2 super-QCD) are discussed from the three different viewpoints: (i) instanton calculus, (ii) N = 2 harmonic superspace, and (iii) M theory. The emphasis is made on the foundations of all three approaches and their relationship.

Journal of High Energy Physics, 2000

The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N = 2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N = 2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions in N = 2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory. We explicitly compute the instanton measure and the contribution to u = Trφ 2 for winding numbers one and two. We then show that each non-perturbative contribution to the N = 2 low-energy effective action can be written as the integral of a total derivative of a function of the instanton moduli. Only instanton configurations of zero conformal size contribute to this result. Finally, the 8k-dimensional instanton moduli space is built using the hyperkähler quotient procedure, which clarifies the geometrical meaning of our approach.

Physical Review D, 1997

Using instanton calculus we check, in the weak coupling region, the nonperturbative relation

Journal of High Energy Physics, 2004

We study (anti-) instantons in super Yang-Mills theories defined on a non anticommutative superspace. The instanton solution that we consider is the same as in ordinary SU (2) N = 1 super Yang-Mills, but the anti-instanton receives corrections to the U (1) part of the connection which depend quadratically on fermionic coordinates, and linearly on the deformation parameter C. By substituting the exact solution into the classical Lagrangian the topological charge density receives a new contribution which is quadratic in C and quartic in the fermionic zero-modes. The topological charge turns out to be zero. We perform an expansion around the exact classical solution in presence of a fermionic background and calculate the full superdeterminant contributing to the one-loop partition function. We find that the one-loop partition function is not modified with respect to the usual N = 1 super Yang-Mills.

Physics Letters B, 1995

We examine the Seiberg-Witten treatment of N = 2 super Yang-Mills theory, and note that in the strong coupling region of moduli space, some massive particle excitations appear to have negative norm. We discuss the significance of our observation.

2003

In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. We present explicit formulas for up to third order on both quantum scales. Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. We also present some non-trivial checks of our results.

Nuclear Physics B, 1983

We calculate some simplest п-point functions in supersyrametric Tang-Mills theories contributed by instantons. The result is not vanishing and we diaeusa some implications of tMs. In particular, the dynamics of the supersyrranetrlc th«oriep rau"t exhibit some unusual featuree. Институт теоретической и ^кспррим^нтчл^ний фя?ики. 4 l (*. ) W £ (*S{ lo r> > ш while in the N=2 case we concentrate on Here W^^V/^-e, B V(/"V;e =-iand W* is the spinor superfield built of the gluon field strength tensor and the gluino field ( see eq.{8)); 3 ie * ne natter scalar superfield and \оУ , lo') are the perturbation theory тасигш states with a unit difference in topological charge. The choice of (1) and (2) is not without motiration. The point is that the change in the topological charge is to be accoepanied by a certain change in chirality. fhe functions (1) and (2) are the simplest ones to satisfy the chirality selection rule. There are some specific problems with instantons in eupereymmetric theories. Superficially, they defy supersynmetry by producing an effective miltifermion interaction without its bosonic counterpart[ J. Although the problem has been erentually resolved \/\ the resolution is not so tririal and calls for integration over the instanton size to recover supersymmetry. Thus, the тегу notion of effective lagrangian induced by inatantons of snail size turns out to be incompatible with the supersynmetry (provided that the underlying classical theory is confomml-invariant, as is the case with gluodynanics). Under the circumstances, it seemed