Saravana Bhavan doesn’t look like a house of secrets. Its dining room at the corner of Lexington Avenue and 26th Street is clean and bright and often attracts a line out front. It doesn’t advertise because it doesn’t need to; the fact that it’s one of the world’s largest chains of vegetarian restaurants — 33 in India, another 47 in a dozen other countries — is considered too obvious to its core clientele of Indian expatriates and tourists to be worth trumpeting.