SO(2N) and SU(N) gauge theories in 2 + 1 dimensions

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Abstract

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N = ∞ limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. It is therefore interesting to know how close is the physics of SO(N) to that of SU(3) for the modest values of N where one might be able to perform chemical potential calculations. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling ’bulk’ transition in 3 + 1 dimensions, we largely confine our numerical calculations to 2 + 1 dimensions in this paper. We provide some analytic estimates of the SO(2N) spectrum in both D = 2 + 1 and D = 3 + 1, and show, numerically, that the D = 2 + 1 SO(6) and SU(4) low-lying spectra do indeed appear to be the same. Our numerical calculations of a number of mass ratios show that the leading O(1/N) correction already dominates for N ≥ 6, and in some cases down to N = 4, and that, as expected, these ratios become consistent with those of SU(N) as N → ∞. In particular we see that SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood.

Keywords

Lattice Gauge Field Theories 1/N Expansion 
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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Physics DepartmentSwansea UniversitySwanseaU.K.
  2. 2.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.

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