Researchers define new, gauge‑invariant observables that live on the boundary of space in string field theory. The construction mirrors a familiar idea from General Relativity called the Brown–York charge, which extracts conserved quantities from a boundary stress tensor. Here the authors start from a recently built gauge‑invariant action for free string field theory with a boundary and use it to produce analogous boundary charges for string fields.

The key technical point is that the variation of the action can vanish in the bulk but leave a nonzero contribution at the boundary. That leftover piece is called a boundary tadpole. Unlike a single number, the tadpole is a state in the string Hilbert space, so the authors show how to pair it with a suitable test state to produce a gauge‑invariant number. Each such number is tied to an