The Glueball Superpotential

Abstract

We compute glueball superpotentials for four-dimensional, N = 1 supersymmetric gauge theories, with arbitrary gauge groups and massive matter representations. This is done by perturbatively integrating out massive charged fields. The Feynman diagram computations simplify, and are related to the corresponding matrix model. This leads to a natural notion of "projection to planar diagrams" for arbitrary gauge groups and representations. We discuss a general ambiguity in the glueball superpotential W (S) for terms, S n , whose order, n is greater than the dual Coxeter number.This ambiguity can be resolved for all classical gauge groups (A, B, C, D), via a natural embedding in an infinite rank supergroup. We use this to resolve some recently raised puzzles. For exceptional groups, we compute the superpotential terms for low powers of the glueball field and propose an all-order completion for some examples including N = 1 * for all simplylaced groups. We also comment on compactification of these theories to lower dimensions.

Supersymmetric gauge theories with flavors and matrix models

“…This puzzle intrigued several papers [19,20,3,15,21,22,23,24]. In particular, in [20], it was found that although N c,i = 0, we cannot set S i = 0.…”

${\mathcal N}=1^*$ MODEL SUPERPOTENTIAL REVISITED (IR BEHAVIOR OF ${\mathcal N}=4$ LIMIT)

“…The last expression has a finite M → 0 limit which is precisely equal to log(A/Λ 3 ) as desired. This "demonstration" only shows that we did not yet establish the exact rule for dealing with "classical" quantities like S ≡ W 2 and their functions, quite apart from the quantum effect discussed in [22]. These problems need further investigations.…”

A note on domain walls and the parameter space of Script N = 1 gauge theories

“…One may then ask how the information about this multiplicity is encoded in four dimensions, if at all? To this end, it is worth recalling the resolution of a (perhaps) analogous puzzle that arises on compactification to 1+1D on a 2-torus (see also [17]). Since we are computing the index tr F (−1) F , one might anticipate that such an additional reduction should not affect the conclusions.…”