SU(N) gauge theory couplings on asymmetric lattices

Frithjof Karsch
1982 Nuclear Physics B  
The connection between euclidean and hamiltonian lattice QCD requires the use of asymmetric lattices, which in turn implies the necessity of two coupling parameters. We analyse the dependence of space-and time-like couplings g" and g~ on the different lattice spacings a and aT in space and time directions. Using the background field method we determine the derivatives of the couplings with respect to the asymmetry factor ~ = a/a~ in the weak coupling limit, obtaining for ~: = 1 the values
more » ... 03, N=2, (0g~2/O~)t~=l = / 0.20161, N = 3, 1-0.06759, N = 2, (0g~2/0~)~=1 =/-0.13195 N = 3. We argue that the sum of these derivatives has to be equal to b0 = 11N/487r 2 and determine the A parameter for asymmetric lattices. In the limit ~ ~ co all our results agree with those of A. and P. Hasenfratz.
doi:10.1016/0550-3213(82)90390-x fatcat:pcsm6ozfcfcl5p7fli6evpzu3m