Softly-broken Script N = 4 supersymmetry in the large-N limit

Abstract

We calculate the exact values of the holomorphic observables of N = 4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve N = 1 SUSY. These include the chiral condensates in each massive vacuum of the theory as well as the central charge which determines the tension of BPS saturated domain walls interpolating between these vacua. Several unexpected features emerge in the large-N limit, including anomalous modular properties under an SL(2, Z) duality group which acts on a complexification of the 't Hooft coupling λ = g 2 N/4π. We discuss our results in the context of the AdS/CFT correspondence.

Curvature singularities: The good, the bad, and the naked

“…Second, they might be massless vacua corresponding to embeddings of SU (2) in SU(N) which leave factors of U(l) unbroken. Third, they might be massive vacua where SU(N) is broken down to some SU(N/p) subgroup by a representation of 577(2) which can be written as N/p blocks of dimension p x p. A recent analysis [57] indicates yet one more possibility. The claim of [57] is that the standard analysis (52) of the gaugino condensate is dramatically altered at strong coupling, and that in the large JV, large QYM^ limit the regular N-gon of vacua for the trivial representation of SU{2) degenerates to points on a line segment.…”

Large N, strings and bag models

“…And so the superpotential, goes like ∼ N 4 . Choosing two generic vacua, the interpolating wall scales like [36,37]:…”

Unoriented strings, loop equations, andN=1superpotentials from matrix models

“…Dorey [34] (see also [47]), following the approach of [48], compactified the theory with SU(N) gauge group on a circle of radius R. The degrees of freedom of the effective 2 + 1-dimensional theory are r = rank(G) complex Abelian scalar fields X a which are composed of the Wilson lines and the scalars dual to the massless photons of the theory.…”