Instantons in aU(1) lattice gauge theory: A Coulomb dipole gas

We study the decompositionA=A _I +A _SW of aU(1) lattice gauge field into instanton and spin wave parts. The action also decomposes,A=A _I +A _SW +R. HereA _I is a Coulomb dipole gas,A _SW is a zero mass free field, andR is a higher order remainder. We studyA _I in detail, ford4, in the dilute gas case (which corresponds to the low temperature limit of the gauge field theory). We establish the leading behavior of the free energy:f ^–d a. Here is the lattice spacing,a is a geometrical constant and is an activity defined in terms of a small number of instanton configurations. Our methods suggest the absence of screening in the dilute dipole gas,d4, in contrast to Debye screening for the dilute monopole gas.Supported in part by the National Science Foundation under Grant PHY 76-17191Supported in part by the National Science Foundation under Grant PHY 75-21212