Duality of nonsupersymmetric largeNgauge theories

Abstract

Starting from Seiberg's electric-magnetic duality for supersymmetric QCD, we construct dual pairs of non-supersymmetric gauge theories. This is accomplished by first taking the large N limit of supersymmetric QCD and it's dual partner and then performing a special "orbifold projection" recently introduced by Kachru and Silverstein. We argue that in the large N limit the two projected theories remain dual. The non-supersymmetric gauge theories which can be studied in this fashion have non-supersymmetric field content, chiral fermions and exactly massless scalar matter.

SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement

“…Firstly, the large N limits of these theories are known to coincide [1] at the diagrammatic level (up to a factor of 2 in g 2 ). Moreover the orbifold equivalence [2][3][4][5][6][7][8][9] between SO(2N ) and SU(N ) gauge theories implies that they have the same physics in the common sector of states when N → ∞ [10,11]. So it would be interesting to confirm these expectations with a non-perturbative lattice calculation of, for example, their common (positive charge conjugation) mass spectra, and also to investigate how SO(2N + 1) gauge theories fit in with this.…”

“…A particular caveat attaches to states in SO (4). If the continuum spectrum is indeed the same as that of SU(2) × SU(2) then there will be states with one glueball from each of the SU(2) groups with a possible shift in mass due to lattice spacing corrections.…”

“…That this holds beyond perturbation theory is something we will test in this paper. Finally we remark that there exists a large-N orbifold equivalence between SO(2N ) and SU(N ) gauge theories [2][3][4][5][6][7][8][9] which has been shown [10,11] to imply that at N = ∞ the theories have the same physics, in their common sector of states. We recall that g 2 has dimensions of mass in D = 2 + 1 and so we can compare dimensionless ratios M i /g 2 N in the different theories, which we will do later on in this paper.…”

“…where the 6 corresponds to the k = 2 antisymmetric representation (which indeed is C = + for SU (4)) and this will map to the fundamental 6 of SO (6). Thus in testing the equivalence of SU (4) and SO (6) we should compare the SO(6) fundamental string tension to the k = 2A string tension in SU(4) which, in terms of the fundamental SU(4) string tension, has the value [16] (see also [28]) σ 2A σ f = 1.357 ± 0.003 ; SU(4).…”

“…Thus in testing the equivalence of SU (4) and SO (6) we should compare the SO(6) fundamental string tension to the k = 2A string tension in SU(4) which, in terms of the fundamental SU(4) string tension, has the value [16] (see also [28]) σ 2A σ f = 1.357 ± 0.003 ; SU(4). (2.11) This implies that when we calculate glueball masses in units of the string tension, the relevant comparison to make is…”