Orbifold Equivalence and the Sign Problem at Finite Baryon Density

Abstract

We point out that SO(2N(c)) gauge theory with N(f) fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential μ(B). One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2N(c)) theory is particularly interesting because a wide class of observables in the SO(2N(c)) theory coincide with observables in QCD in the large N(c) limit, as we show using the technique of large N(c) orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at finite μ(B) provided one adds appropriate deformation terms to the SO(2N(c)) theory. This opens up the prospect of learning about QCD at finite μ(B) using lattice studies of the SO(2N(c)) theory.

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.…”

“…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…”

“…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. Secondly, certain low N pairs of theories possess the same Lie algebras: SU (2) and SO(3); SU(2) × SU(2) and SO(4); SU(4) and SO (6). Again it would be interesting to know if the spectra are the same or if the differences in the global properties of the groups, to which large fields may be sensitive, influence the spectrum.…”