D-brane effective field theory from string field theory
Washington Taylor
TL;DR
The paper demonstrates that open bosonic string field theory, approached via level truncation, yields convergent, quantitative predictions for quartic terms in the D-brane effective action, specifically for the tachyon $\phi$ and the gauge field $A^{\mu}$ through terms $\phi^4$, $(A^{\mu}A_{\mu})^2$, and $[A_{\mu},A_{\nu}]^2$. Integrating out massive modes up to level $n\le 20$ produces results within about 2–4% of the known exact values, and reveals that gauge-violating spurions from the tachyon are largely canceled by higher-level contributions, leaving a gauge-invariant nonabelian Born–Infeld-like structure in the zero-momentum sector. The work also outlines extensions to compute higher-order nonabelian terms, discusses possible formulations of nonabelian Born–Infeld in string theory, and connects tachyon condensation in string field theory with unstable vacua in Yang–Mills and Born–Infeld theories, including a concrete brane model illustrating the dual pictures. These results bolster the viability of string field theory as a tool to derive and understand effective D-brane actions and their nonperturbative dynamics.
Abstract
Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms φ^4, (A^μA_μ)^2 and [A_μ, A_ν]^2 for the zero momentum tachyon and gauge field on one or many bosonic D-branes. We find that the level truncation method converges for these terms within 2-4% when all massive fields up to level 20 are integrated out, although the convergence is slower than exponential. We discuss the possibility of extending this work to determine the structure of the nonabelian Born-Infeld theory describing the gauge field on a system of many parallel bosonic or supersymmetric D-branes. We also describe a brane configuration in which tachyon condensation arises in both the gauge theory and string field theory pictures. This provides a natural connection between recent work of Sen and Zwiebach on tachyon condensation in string field theory and unstable vacua in super Yang-Mills and Born-Infeld field theory.