The prepotential of SU(2)×SU(2) supersymmetric Yang–Mills theory with bifundamental matter

Abstract

We study the non-perturbative, instanton-corrected effective action of the N = 2 SU(2) × SU(2) supersymmetric Yang-Mills theory with a massless hypermultiplet in the bifundamental representation. Starting from the appropriate hyperelliptic curve, we determine the periods and the exact holomorphic prepotential in a certain weak coupling expansion. We discuss the dependence of the solution on the parameter q = Λ 2 2 Λ 1 2 and several other interesting properties. * Ulrike.Feichtinger@cern.ch

Prepotential and instanton corrections in Script N = 2 supersymmetric SU(N1) × SU(N2) Yang Mills theories

“…They compute up to the third instanton correction using the fact that for this particular case the curve is still hyperelliptic, so one can use the standard Picard-Fuchs techniques to calculate the instanton corrections. We have checked that our results for that case listed in (4.20) agree with those presented in [26].…”

“…For higher instanton corrections the only result available in the literature is the one in [26] for the case SU (2) × SU (2). They compute up to the third instanton correction using the fact that for this particular case the curve is still hyperelliptic, so one can use the standard Picard-Fuchs techniques to calculate the instanton corrections.…”

Instantons on Quivers and Orientifolds

“…The result (3.8,3.7) are indeed in perfect agreement with formula (27,28) in [17] after (B.1) is taken into account (see also [19]). Our formulae can also be tested against the results in [18] for the SU(2) × SU(2) with a single bifundamental matter. Given that the v.e.v.…”

“…We are able to treat a wide range of models: massive or massless with various matter content. The largest formulae are confined in appendices B, C. Appendix B is a check against existing literature [17,18,19]. Finally in Section 4, instead of modding by a discrete group, we introduce an orientifold plane in the D(-1)-D3-brane system.…”

“…18) and ℓ αβ (s) is the "length of the hook stretched between the tableaux Y α , Y β " and centered on the box s ∈ Y α . More precisely ℓ αβ (s) is the standard hook length for a box s ∈ Y α…”