Closed Superstring Field Theory and its Applications

TL;DR

The work advances a covariant, quantum-consistent framework for closed superstring field theory (heterotic and Type II) that renders S-matrix amplitudes finite and unitary above five non-compact dimensions by systematically addressing tadpoles and mass renormalization through a BV-master action and a vacuum-shift analysis. It develops off-shell amplitudes via a world-sheet Omega-form on an extended P-space, governs them with a gauge-fixed action, and enforces Ward identities and 1PI/effective actions to control divergences and organize perturbation theory. It then analyzes the quantum-corrected vacuum, global and local symmetries in the shifted background, and formulates a momentum-space, Wilsonian perspective that yields a robust unitarity proof via Cutkosky rules, while highlighting the role of stubs and PCO prescriptions. The framework is applied to Calabi–Yau compactifications (SO(32) heterotic) and discusses extensions, limitations, and connections to alternative formalisms, providing a comprehensive toolkit for perturbative, covariant superstring dynamics with clear avenues for further computation and background independence questions.

Abstract

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 non-compact space-time dimensions, but suffers from the usual infrared divergences when the number of non-compact space-time dimensions is 4 or less.

Figures (24)

• Figure 1: The left figure shows a Riemann surface near a separating type degeneration and the right figure shows a Riemann surface near a non-separating type degeneration. The degeneration happens when $S_1$ and $S_2$ shrink to a point.
• Figure 2: The left figure shows the Feynman diagrams in field theory analogous to a separating type degeneration and the right figure shows the Feynman diagrams in field theory analogous to a non-separating type degeneration. The blobs represent arbitrary Feynman diagrams, and the thick lines represent propagators whose Schwinger parameters go to infinity in the degeneration limit.
• Figure 3: A tree level diagram that encounters type 1 divergence when the total energy flowing along the horizontal line exceeds the threshold for producing an on-shell single particle intermediate state.
• Figure 4: The figure on the left shows a divergence associated with massless tadpoles. The thick line is forced to carry zero momentum due to momentum conservation. Therefore if it represents a massless particle, the propagator diverges. The diagram on the right shows divergences associated with mass renormalization. Requiring the external line to be on-shell also puts the internal line marked by the thick line on-shell, causing a divergence.
• Figure 5: The space $\widetilde{{\cal P}}_{g,m,n}$ as a fiber bundle.