An exact relation for orientifold field theories with arbitrary superpotential

Abstract

We discuss a nonperturbative relation for orientifold parent/daughter pairs of supersymmetric theories with an arbitrary tree-level superpotential. We show that super-Yang-Mills (SYM) theory with matter in the adjoint representation at N → ∞, is equivalent to a SYM theory with matter in the antisymmetric representation and a related superpotential. The gauge symmetry breaking patterns match in these theories too. The moduli spaces in the limiting case of a vanishing superpotential are also discussed. Finally we argue that there is an exact mapping between the effective superpotentials of two finite-N theories belonging to an orientifold pair.

Discrete and oscillatory matrix models in Chern–Simons theory

“…6, closer to the Wigner-Dyson case were the oscillations are of smaller amplitude and are essentially smoothed out when N is very large. (36)- (37) with q = 0.9, N = 100 models may be related to recent findings in N = 1 gauge theory [9,10,11] (see [43] for a review on planar equivalence of related theories). More precisely, these works show that different N = 1 supersymmetric gauge theories can have an effective glueball superpotential with exactly the same functional form.…”

“…Interestingly enough, it seems that this non-uniqueness also leads to the equivalence of effective superpotentials in N = 1, through a rather different route from [9,10,11]. A further understanding of this seems desirable.…”

“…From a mathematical point of view, it is remarkable that the potential may be so wild even to reach fractal behavior and still leave the partition function (which in addition is a Chern-Simons partition function) unchanged. Interpretations in terms of gauge theories and quantum groups are discussed in some instances, and we show that the equivalence of potentials of the (generalized) Chern-Simons matrix models introduced, leads to a complementary view of the equivalence of effective superpotentials in N = 1 supersymmetric gauge theories [9,10,11]. In the last section, we comment on the possible physical relevance and some further avenues of research are suggested.…”

“…In this paper, we shall focus on the matrix models that appear in Chern-Simons theory [5,6] and also discuss the recently found connection with 2dYM [7,8] as well as N = 1 supersymmetric gauge theories. More precisely, with recent work that discusses the equivalence of effective superpotentials in these theories [9,10,11].…”

Equivalence of effective superpotentials

“…In fact, the present investigation was spurred by the conjectured equivalence of the effective superpotentials in this latter case in [5], conjecture based on the orientifold parent-daughter relation between the theory with the adjoint and the one with the antisymmetric. For U3, it becomes a relation between theories with adjoint and with fundamental matter.…”