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Symplectic structure in open string field theory II: Sliding lump

Vinícius Bernardes, Theodore Erler, Atakan Hilmi Fırat

TL;DR

This work develops a concrete Hamiltonian perspective on open string field theory by deriving a new phase-space symplectic structure for boosted solitonic lumps. The authors obtain a mass formula ${m = \dfrac{1}{g^2} \mathrm{Tr}_{Q\sigma}[(i J^{01} \Psi)(i p_1 \Psi)]}$ and demonstrate, via an analytic D0-lump, that the resulting D-brane tension matches the on-shell action through an $L_\infty$ coalgebra framework. They resolve divergences inherent in twist-field-based constructions by a divergence-free sigmoid built from a lightlike boson, and compute the lump mass explicitly as ${m = \dfrac{Z_{\mathrm{D0}}}{\mathrm{vol}(X^0)} \dfrac{1}{2\pi^2 g^2}}$, confirming the expected D0-brane tension. The final general boosted-solution analysis shows the mass is equivalent to the on-shell action expansion around a boost-invariant vacuum, establishing a robust link between Hamiltonian observables and on-shell dynamics in open SFT.

Abstract

We use a new formula for symplectic structure to compute the momentum of an analytic lump solution moving at constant velocity in Witten's open string field theory. The computation gives a new way to determine the D-brane tension in string field theory. Using homotopy algebra technology, we prove that this tension must agree with the value implied by the on-shell action.

Symplectic structure in open string field theory II: Sliding lump

TL;DR

This work develops a concrete Hamiltonian perspective on open string field theory by deriving a new phase-space symplectic structure for boosted solitonic lumps. The authors obtain a mass formula and demonstrate, via an analytic D0-lump, that the resulting D-brane tension matches the on-shell action through an coalgebra framework. They resolve divergences inherent in twist-field-based constructions by a divergence-free sigmoid built from a lightlike boson, and compute the lump mass explicitly as , confirming the expected D0-brane tension. The final general boosted-solution analysis shows the mass is equivalent to the on-shell action expansion around a boost-invariant vacuum, establishing a robust link between Hamiltonian observables and on-shell dynamics in open SFT.

Abstract

We use a new formula for symplectic structure to compute the momentum of an analytic lump solution moving at constant velocity in Witten's open string field theory. The computation gives a new way to determine the D-brane tension in string field theory. Using homotopy algebra technology, we prove that this tension must agree with the value implied by the on-shell action.

Paper Structure

This paper contains 5 sections, 153 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Sliding Lump
  3. Symplectic structure
  4. Lump mass
  5. General boosted solution

Figures (2)

  • Figure 4.1: When evaluating the mass formula (\ref{['eq:m']}) using the analytic lump solution, Neumann-Dirichlet twist fields $\sigma_\text{ND},\overline{\sigma}_\text{ND}$ collide and pinch the endpoints of the translation and boost generators, creating a logarithmic divergence.
  • Figure 4.2: Correlation function on the cylinder described in (\ref{['eq:psOs']}). The cylinder is illustrated as a semi-infinite strip where the left and right edges are glued. The complex plane is shown so that the positive real axis increases to the left, which is natural in the left handed star product convention Erler2. Note that different segments of the open string boundary carry D1-brane or D0-brane boundary conditions.