Gravitational instantons from closed superstring field theory

We test exact marginality of the deformation describing the resolution of a $\mathbb{Z}_2$ orbifold by analyzing the closed superstring equations of motion to third order in the size, including $α’$ corrections. We find that the third order correction is unobstructed for all deformation moduli. We are also able to reproduce the Eguchi-Hanson gravitational instanton up to the second order in the field theory limit with a suitable choice of moduli.

💡 Research Summary

The paper investigates whether the deformation that resolves the ℤ₂ orbifold singularity of C²/ℤ₂ is an exactly marginal deformation in closed superstring theory. Using the framework of closed superstring field theory (SFT) with its L∞ algebraic structure, the authors perform a systematic perturbative expansion of the string field Ψ in a dimensionless parameter λ, where the first-order term Ψ^(1) corresponds to the marginal vertex operator built from the twisted sector twist fields.

The SFT action is written as a cyclic L∞ functional: S