Background-field quantization and the light-cone planar gauge: An exception to Kallosh’s theorem

The one-loop vacuum-polarization tensor for pure Yang-Mills theory is examined using background-field quantization in the light-cone planar gauge, i.e., with the gauge-fixing Lagrangian scrLgf =(1/2{α})n{·}Qᵃ{D}²ᵃᵇ(A)n·{Q}ᵇ$, where ${n}²$=0. The divergent part of the vacuum polarization, [${{Π}}_{{μ}{ν}}$(p${)]}div, is found to depend on both α and{n}_{{μ}}$, and hence is gauge dependent. This result does not comply with Kallosh's theorem, according to which the counterterms should be independent of gauge choice. We argue that the occurrence of nonlocal counterterms in the light-cone-type gauges violates one of the implicit assumptions of Kallosh's theorem. We also point out that a similar violation of Kallosh's theorem occurs also in the ordinary light-cone gauge, i.e., using the gauge-fixing Lagrangian scrL_gf=-(1/2α)(n·Q)², where n²=0.