Which nerve is responsible for registering pain in the pulp cavity?

The trigeminal nerve is the primary nerve responsible for sensation in the face, including pain transmission from the pulp cavity of the teeth. It has three major branches: the ophthalmic, maxillary, and mandibular nerves. Specifically, the maxillary and mandibular branches innervate the teeth, providing sensory information related to pain, temperature, and touch. When the pulp of a tooth becomes inflamed or irritated, the trigeminal nerve transmits signals from the affected area to the brain, where they are interpreted as pain.

The other nerves listed do not primarily function in the sensory perception of the oral cavity. The vagus nerve is involved in autonomic functions such as heart rate and digestion, the facial nerve primarily controls facial expressions and carries taste sensations from the anterior tongue, and the spinal accessory nerve innervates neck muscles and does not contribute to tooth sensation. Thus, the trigeminal nerve's role in transmitting dental pain makes it the correct answer.