Since its formulation in 1948 by Richard Feynman, the Feynman diagram technique has become an indispensable tool in quantum field theory (or QFT) for performing perturbative calculations. In modern times, the Feynman diagram also serves as a guide in formulating string theory (a theoretical framework that unifies gravity with the other fundamental forces) in the style of QFT. However, the Feynman diagram is based on a point-particle view, while a string field theory (or SFT) has one-dimensional strings as its degrees of freedom. Moreover, calculation in SFT using Feynman diagrams is not as convenient as in the case of QFT. Could there exist a framework unique to SFT that provides a new interpretation of the perturbative calculations?

Guided by this intuition, physicists from Czech Academy of Sciences, in a new study, found a different way of expressing the “on-shell” scattering amplitude in cubic open SFT, the simplest version of open SFT formulated by Ed Witten, which did not appear to have a counterpart in QFT.

The key to finding this new formula was gauge symmetry and the concept of the “tachyon vacuum,” which, in open SFT, means a system without D-branes, as Ashoke Sen pointed out in 1999. Using this tachyon vacuum as the building block, the researchers expressed the formula as a function of the difference between the classical solution representing the D-brane system (for which they wanted to calculate the amplitude) and the classical solution for the tachyon vacuum, such that it remained invariant under the gauge transformation of each classical solution.

Discovering such new structures and formulas will make SFTs as easy to use as QFTs, which could lead to a better understanding of string theory and, eventually, to a deeper understanding of our universe at the most fundamental level.