Background Fields in String Theory In "String theory and M-theory" (K. Becker, M. Becker and H.Schwarz) page 81, they said that among the background fields, the fields associated with massless bosonic fields are especially significant. My question is, why is that? What's the most general form for the action in bosonic string theory with background theory if all fields are included?
Thank you!
 A: Bosonic fields are "more significant" than fermionic fields because they may get large vacuum expectation values – from a condensate of many bosons in the same state. Consequently, there may exist a meaningful classical field theory limit.
Massless fields are "more significant" than massive fields because the massive fields in string/M-theory because the massive ones have masses of order the string scale or the Planck scale which is huge and at these short distances or high energies, the classical reasoning breaks down, anyway. So we apply the classical effective equations of motion only at distances much longer than the string or Planck scale and at these low energies, only the massless fields are visible (the massive fields can't be excited so they're "integrated out" and don't appear in the action).
Becker-Becker-Schwarz try to jump to the truly consistent full theory, which is the supersymmetric one, as quickly as they can so the general bosonic string theory's effective action may be absent in the book. But the corresponding action for the superstring theory is on page 311 etc. – type II supergravity. Borrow another textbook such as Polchinski if your primary interest is bosonic string theory. There are kinetic and potential terms for the tachyon, some kinetic terms for the dilaton, the Einstein-Hilbert action for the metric tensor, and some natural "squared field strength" from the $B$-field. Strictly speaking, the tachyon terms should be removed if we talk about "massless fields" because the tachyon field isn't massless. But because of its negative squared mass, it's even "less massive" than the ordinary massive states as well as the massless states – it's "below" the massless level – so we usually do include it, too.
