[Paper Review] On the relevance of tachyons

Jeffrey A. Harvey, David Kutasov+1 more|ArXiv.org|Mar 13, 2000

Black Holes and Theoretical PhysicsPhysics and Astronomy35 references91 citations

TL;DR

This paper proposes that boundary renormalization group (RG) flows in the worldsheet theory provide a simple and exact framework for understanding open string tachyon condensation. By analyzing RG flows induced by boundary perturbations—specifically the Sine-Gordon model—it shows that tachyon condensation leads to the complete disappearance of open string modes and the formation of lower-dimensional D-branes, with the boundary entropy $ g $ decreasing monotonically, consistent with the $ g $-theorem and confirming that unstable D-branes annihilate into the closed string vacuum.

ABSTRACT

We study condensation of open string tachyons using renormalization group flow in the worldsheet field theory. This approach leads to a simple picture of the physics of the nontrivial condensate.

Motivation & Objective

• To provide a conceptual and quantitative framework for understanding tachyon condensation in open string theory using worldsheet renormalization group (RG) flows.
• To clarify why level-truncated string field theory calculations yield rapidly convergent results for vacuum energy and spectrum.
• To demonstrate that tachyon condensation leads to the complete disappearance of open string modes and the formation of lower-dimensional D-branes.
• To establish a connection between boundary RG flows and the physical properties of nontrivial vacua in string theory, including the behavior of boundary entropy $ g $.
• To extend the analysis to non-BPS D-branes and closed string tachyon condensation, showing analogous localization and reduction of degrees of freedom.

Proposed method

• Analyzes boundary RG flows in the open bosonic string using the Sine-Gordon model as a boundary perturbation $ T[X_{25}] = -\lambda \cos[kX_{25}] $.
• Uses exact solutions via the thermodynamic Bethe ansatz (TBA) to compute the boundary entropy $ g $ in the UV and IR limits.
• Applies the $ g $-conjecture, showing $ g_{\text{IR}}/g_{\text{UV}} = k $, which matches the ratio of D-brane tensions.
• Compares conformal perturbation theory with level-truncated string field theory, explaining rapid convergence via RG improvement.
• Extends the analysis to non-BPS D-branes by considering complex combinations of boundary fields and massless modes.
• Applies the same framework to closed string tachyon condensation, showing localization of all string modes in lower-dimensional spacetime.

Experimental results

Research questions

• RQ1 How does the boundary RG flow explain the condensation of open string tachyons and the resulting disappearance of D-branes?
• RQ2 Why do level-truncated string field theory calculations converge so rapidly to the correct vacuum energy and spectrum?
• RQ3 What is the role of boundary entropy $ g $ in characterizing the number of D-brane degrees of freedom during tachyon condensation?
• RQ4 How does the worldsheet RG approach describe the formation of lower-dimensional D-branes from unstable D-brane systems?
• RQ5 Can the same RG framework be applied to closed string tachyon condensation, and what are the resulting spacetime properties?

Key findings

• The boundary RG flow with a relevant Sine-Gordon perturbation leads to a decrease in boundary entropy $ g $, with $ g_{\text{IR}}/g_{\text{UV}} = k $, matching the ratio of D24-brane to D25-brane tensions.
• All open string modes disappear from the spectrum in the IR, confirming that tachyon condensation leads to a complete annihilation of the D-brane.
• The IR fixed point corresponds to a stack of D24-branes, with the boundary value of $ X_{25} $ pinned to minima of the cosine potential, spaced $ 2\pi/k $ apart.
• The $ g $-theorem is verified in this exact solution, showing $ g $ decreases monotonically along the flow, consistent with the conjecture.
• For $ k^2 = 1 $, the perturbation is marginal and $ g $ is constant, corresponding to a line of fixed points interpolating between Neumann and Dirichlet boundary conditions.
• The framework generalizes to non-BPS D-branes, where one combination of boundary fermions remains massless, allowing for a non-GSO projected spectrum in the IR.