It should be host DNA polymerase. Read below:
Early transcription (the mRNAs made during this phase are the alpha and beta mRNAs) (figure 16)
Herpes viruses use host RNA polymerase. However, a virion protein (VP16) enters the nucleus upon infection and is important as part of the transcription factor complex recognized by the host RNA polymerase. The virus uses host mRNA modification enzymes.
Initially, alpha-mRNAs are transcribed. These are the immediate early mRNAs and are exported to the cytoplasm and translated into alpha-proteins. The α-proteins translated in the cytoplasm are transported into nucleus where they enable the beta-promoters to be used by the host RNA polymerase (figure 16).
Beta-mRNAs are transcribed the by host RNA polymerase. (Beta-genes are still "early" since they are transcribed prior to DNA synthesis. Sometimes therefore, alpha-genes are called "immediate early" and beta-genes are called "early"). Beta proteins are involved in gene expression regulation. They decrease alpha-gene expression and are needed for gamma gene expression. They are also involved in various aspects of DNA synthesis; for example, herpes beta -genes code for:
DNA polymerase
DNA binding proteins
thymidine kinase
ribonucleotide reductase
SINCE THESE BETA PROTEINS ARE VIRALLY-CODED AND NOT HOST-CODED ENZYMES, THEY ARE POTENTIALLY WEAK LINKS IN THE VIRUS LIFE CYCLE AND THUS PROMISING TARGETS FOR VIRAL CHEMOTHERAPY