(In)validity of largeNorientifold equivalence

Abstract

It has been argued that the bosonic sectors of supersymmetric SU (N ) YangMills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the N → ∞ limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N ) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N "orientifold equivalence" have appeared. By considering theories compactified on R 3 × S 1 , we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration. Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whether or not this condition is satisfied on R 4 (or R 3 × S 1 for sufficiently large radius) is not currently known.

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

“…As discussed in section 2.2.2 the fundamental SO(6) string tension corresponds to the k = 2a SU(4) string tension and the SO(6) coupling is related to the SU (4) which is entirely consistent with the directly calculated SU(4) value √ σ k=2a /g 2 =0.8833 (11).…”

“…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.…”

“…(We use the values of aM 0 + in tables 20-27 and the plaquette values in tables [11][12][13][14][15][16][17][18].) It turns out that we can obtain reasonable fits to all our lattice data using just the leading O(1/β I ) correction, and the results of these fits are listed in table 30.…”

“…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.…”

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model

“…This confinement mechanism may remain responsible for the confinement at strong-coupling regime due to the continuity principle. This argument is also of importance in terms of the recent progress in large-N volume reduction [30][31][32][33][34][35][36][37][38][39][40]. On the other side, neutral bions (zero topological charge and zero magnetic charge) can be identified as the infrared renormalon [10][11][12][13][14][15][16][17][18][19][41][42][43].…”