Abstract
We investigate whether one can observe in SO(3) and SO(4) (lattice) gauge theories the presence of spinorial flux tubes, i.e. ones that correspond to the fundamental representation of SU(2); and similarly for SO(6) and SU(4). We do so by calculating the finite volume dependence of the Jp = 2+ glueball in 2 + 1 dimensions, using lattice simulations. We show how this provides strong evidence that these SO(N) gauge theories contain states that are composed of (conjugate) pairs of winding spinorial flux tubes, i.e. ones that are in the (anti)fundamental of the corresponding SU(N′) gauge theories. Moreover, these two flux tubes can be arbitrarily far apart. This is so despite the fact that the fields that are available in the SO(N) lattice field theories do not appear to allow us to construct operators that project onto single spinorial flux tubes.
Highlights
Lattice preliminariesOur lattice calculations are standard and we refer to [4] for a detailed description of the SU(N ) calculations, and to [1] for details of our SO(N ) calculations
Be constructed from tensor products of the SO(6) fundamental representation
We investigate whether one can observe in SO(3) and SO(4) gauge theories the presence of spinorial flux tubes, i.e. ones that correspond to the fundamental representation of SU(2); and for SO(6) and SU(4)
Summary
Our lattice calculations are standard and we refer to [4] for a detailed description of the SU(N ) calculations, and to [1] for details of our SO(N ) calculations. To calculate the excited states En in eqn (2.2), one calculates (cross)correlators of several operators and uses these as a basis for a systematic variational calculation in e−Ht0 where H is the Hamiltonian (corresponding to our lattice transfer matrix) and t0 is some convenient distance. (Typically we choose t0 = a.) To have good overlaps onto the desired states, so that one can evaluate masses at values of t where the signal has not yet disappeared into the statistical noise, one uses blocked and smeared operators. [1, 4].) For SO(N ) at the smallest values of N , these operators, as used in [1], do not have very good overlaps onto the desired states. What we mean by this is that when one calculates the continuum limits of μ/g2 in SO(N ) and in SU(N ) they are equal within errors once one relates the two values of g2 by the theoretically predicted factors [1]
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