Inversion Symmetry of Gravitational Coupling in Cubic String Field Theory

Understand

It was found that the canonical energy of multi-brane solutions in CSFT constructed by the KBc algebra has a symmetry under the exchange of K=0 and K=\infty (inversion symmetry).

• On the other hand, the gauge invariant observable (GIO), which is regarded as the energy defined by the gravitational coupling of open string, cannot count the energy from K=\infty and therefore is not equal to the canonical energy.
• To resolve this discrepancy, we examine the recent argument of Baba and Ishibashi which directly relates the two energies.
• We find that the gravitational coupling which is equivalent to the canonical energy consists of the GIO and another new term, and the whole has the inversion symmetry.