Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

String Field Theory Around the Tachyon Vacuum

Leonardo Rastelli, Ashoke Sen, Barton Zwiebach

TL;DR

The paper argues that near the tachyon vacuum the kinetic term of cubic open string field theory can be taken as ghost-only, yielding a gauge-invariant action with no open-string excitations. It posits a universal ghost-based kinetic operator of the form $Q= obreak\sum a_n C_n$, with $C_n=c_n+(-1)^n c_{-n}$, and argues such a form can be related by field redefinitions to the conventional BRST formulation. By analyzing tachyon Green's functions and invoking analyticity assumptions, it derives lump solutions of codimension and computes tension ratios that match the known D-brane tensions, with the crucial result that a function $B( ext{alpha})$ vanishes numerically. The work discusses normalization, gauge fixing, level truncation, and extensions to superstrings and closed strings, outlining open questions and potential implications for nonperturbative open-string dynamics.

Abstract

Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The key ingredients in this analysis are certain assumptions about the analyticity properties of tachyon Green's functions. With the help of some further assumptions about the properties of these Green's functions, we also calculate the ratios of tensions of lump solutions of different dimensions. The result is in perfect agreement with the known answers for the ratios of tensions of D-branes of different dimensions.

String Field Theory Around the Tachyon Vacuum

TL;DR

The paper argues that near the tachyon vacuum the kinetic term of cubic open string field theory can be taken as ghost-only, yielding a gauge-invariant action with no open-string excitations. It posits a universal ghost-based kinetic operator of the form , with , and argues such a form can be related by field redefinitions to the conventional BRST formulation. By analyzing tachyon Green's functions and invoking analyticity assumptions, it derives lump solutions of codimension and computes tension ratios that match the known D-brane tensions, with the crucial result that a function vanishes numerically. The work discusses normalization, gauge fixing, level truncation, and extensions to superstrings and closed strings, outlining open questions and potential implications for nonperturbative open-string dynamics.

Abstract

Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The key ingredients in this analysis are certain assumptions about the analyticity properties of tachyon Green's functions. With the help of some further assumptions about the properties of these Green's functions, we also calculate the ratios of tensions of lump solutions of different dimensions. The result is in perfect agreement with the known answers for the ratios of tensions of D-branes of different dimensions.

Paper Structure

This paper contains 15 sections, 87 equations, 3 figures.

Table of Contents

  1. Introduction and Summary
  2. String Field Theory Around the Tachyon Vacuum
  3. Algebraic structure before and after condensation
  4. An ansatz for the SFT after condensation
  5. The Lump Solutions and Their Tensions
  6. Analysis of the tachyon effective action
  7. Setup for lump solutions
  8. Solving the lump equations
  9. Computation of ratios of lump tensions
  10. Further studies and open questions
  11. On the uniqueness of ${\cal Q}$
  12. On the use of level truncation
  13. On gauge fixing
  14. On superstring field theory and closed strings
  15. Concluding remarks

Figures (3)

  • Figure 1: The function $A(\alpha)$ for $n=50$ (dashed) and $n=500$ (continuous). Actually the error is so small that the lines are essentially on top of each other.
  • Figure 2: The function ${\cal B} (n,\alpha)$ (equation (\ref{['cB']})) plotted for $n=50$ (dashed) and $n=500$ (continuous).
  • Figure 3: The function $C(\alpha)$ (eqn. (\ref{['e35']})) for $n=50$ (dashed) and $n=500$ (continuous). Actually the error is so small that the lines are essentially on top of each other.