Improved superlinks for higher spin glueballs

Traditional smearing or blocking techniques serve well to increase the overlap of operators onto physical states but allow for links orientated only along lattice axes. Recent attempts to construct more general propagators have shown promise at resolving the higher spin states but still rely on iterative smearing. We present a new method of superlink construction which creates smeared links from (sparse) matrix multiplications, allowing for gluonic propagation in arbitrary directions. As an application and example, we compute the positive-parity, even-spin glueball spectrum up to spin 6 for pure gauge SU(2) at $\beta =6$, $L=16$, in $D=2+1$ dimensions.

Figure 1

Superlinks of various widths and orientations. The superlink along the central line contains contributions from all the links covered by the surrounding shaded region.

Figure 2

Operators for Polyakov loops at sizes 1, 2, and 4.

Figure 3

Box operators at sizes 1, 2, 3, 4, 5, 6, and 7.

Figure 4

Bar operators at sizes 2, 5, and 7.

Figure 5

8-fold points at sizes 1, 2, 3, and 4.

Figure 6

8-fold operators at sizes 1, 2, 3, and 4.

Figure 7

12-fold clock points at sizes 1, 2, 3, 4, 5, 6, and 7. Note the redundancy in corner points for size 1 and between sizes 3 and 4.

Figure 8

12-fold rhomboid operators at sizes 2, 4, 5, 6, and 7.