For the vast majority of a herpesvirus infection, the virus genome is only present in the nucleus of latently-infected neuronal cells; there are no virus particles in the body. My understanding is that there will therefore be no circulating antibodies unless the latently infected neurons reactivate and begin producing viral particles. However, in this 2005 review, "Immunity in latent Herpes simplex virus infection", mouse studies found that infected neurons had CD8+T cells stuck to them that stayed there and secreted interferons for the lifetime of the animal:
In mice, CD8+T cells invade TG ~7 days after HSV-1
infection, reach maximum ~4 days p.i. and are then retained
in a significant number seemingly for the life-time of the
animal. Significantly, HSV-1-specific CD8+T cells are
persistently stimulated within the latently infected TG. ... The steady expression of IFN-γ and TNF-α in latently
infected TG suggests continuous stimulation of the cells
producing these cytokines. Expression of these cytokines is
tightly regulated and subsides within two hours of
withdrawal of the stimulant. Since IFN-γ can block HSV-1
reactivation from latency in sensory neurons, such a CD8+T
cell population is ideally suited to the function of long-term
protection with minimal tissue destruction (Kodukula et al.,
1999; Liu et al., 2000, 2001; Mueller et al., 2003; Stuart et
So this implies it's the presence of T-cells in the trigeminal ganglion (TG in the above quote) that keeps infected neurons from reactivating and producing new virus. Since the T-cells are apparently being continuously stimulated, it seems possible that B-cells could also be getting stimulated and secrete antibodies, but I haven't seen that possibility addressed anywhere. Also, this continuous stimulation of the immune cells may only happen in mice, not in human infections:
In contrast to latently HSV-1-infected mice,
the frequent reactivation of HSV-1 in human TG may reflect
a less efficient CD8+T cell recognition. This would be
compatible with the fact that HSV-1 ICP47 protein inhibits
TAP-mediated transport of antigenic peptides more
efficiently in human than in mouse cells.
Mice with suppressed B-cells were not found to be less effective at preventing reactivation of latent HSV-1 infections.
Finally, the viral antigen that most of the reactivation-inhibiting T-cells were found to be going after was a fragment of gB, an envelope glycoprotein somewhat similar to the famous coronavirus spike protein. I would expect this antigen to also be a major target for antibodies.