[Paper Review] On decay of Bulk Tachyons

Takao Suyama|ArXiv.org|Aug 5, 2003

Black Holes and Theoretical Physics8 references5 citations

TL;DR

This paper investigates the decay of bulk tachyons in bosonic and Type 0 string theories compactified on a circle, showing that the tachyon potential has a local minimum due to finite four-point coupling constants. The classical evolution of the tachyon-graviton-dilaton system leads to a runaway dilaton, indicating strong coupling; however, conjectured strong coupling endpoints in these theories suggest the decay may terminate in a stable, supersymmetric theory.

ABSTRACT

We investigate a decay of a bulk tachyon with a Kaluza-Klein momentum in bosonic and Type 0 string theories compactified on S^1. Potential for the tachyon has a (local) minimum. A decay of the tachyon would lead the original theory to a strongly coupled theory. An endpoint of the decay would exist if the strong coupling limit exists and it is a stable theory.

Motivation & Objective

• To understand the decay dynamics of bulk tachyons in non-supersymmetric string theories compactified on $S^1$.
• To determine the shape of the tachyon potential in the low-energy effective theory using on-shell scattering amplitudes.
• To analyze classical solutions of the tachyon-graviton-dilaton system to explore the endpoint of tachyon decay.
• To investigate whether the strong coupling regime reached during decay corresponds to a stable, supersymmetric endpoint in Type 0 and bosonic string theories.

Proposed method

• Use Kaluza-Klein compactification on $S^1$ to make certain tachyon modes massless, enabling computation of four-point scattering amplitudes.
• Calculate the four-point coupling constant for tachyons from on-shell amplitudes in the massless limit, using vertex operators with Kaluza-Klein momenta.
• Derive the effective potential for the tachyon by analyzing the amplitude's behavior under small radius deformations, inferring the potential shape for nearly massless tachyons.
• Solve the classical equations of motion for the tachyon, dilaton, and graviton in the low-energy effective theory to study the time evolution of the system.
• Apply conjectured strong coupling limits of Type 0 and bosonic string theories to identify a possible stable endpoint of the decay process.
• Use T-duality and orbifold constructions to compare spectra and support the conjectured endpoint behavior in Type 0 theories.

Experimental results

Research questions

• RQ1 Does the tachyon potential in compactified bosonic and Type 0 string theories have a local minimum?
• RQ2 What is the shape of the tachyon potential derived from four-point scattering amplitudes in the massless limit?
• RQ3 How does the classical evolution of the tachyon-graviton-dilaton system behave, particularly regarding the dilaton field?
• RQ4 Can the strong coupling regime reached during tachyon decay be identified as a stable, supersymmetric endpoint in these theories?
• RQ5 What is the role of Kaluza-Klein modes in enabling the computation of tachyon potential parameters via on-shell amplitudes?

Key findings

• The four-point coupling constant for the tachyon is positive and finite in the massless limit, indicating a local minimum in the tachyon potential.
• The tachyon potential remains finite and non-zero even when the compactification radius is slightly deformed, confirming the existence of a local minimum for nearly massless tachyons.
• Classical solutions of the tachyon-graviton-dilaton system show the dilaton field grows without bound, signaling a transition to a strongly coupled regime.
• The strong coupling limit of Type 0 string theory is conjectured to be a stable, supersymmetric theory, suggesting the tachyon decay may end at a stable endpoint.
• In Type 0A theory, the strong coupling limit is conjectured to be equivalent to M-theory on a Melvin background with $2 au$ rotation, supporting the existence of a stable endpoint.
• The spectrum of Type IIA on $S^1/t^{1/2} imes (-1)^{F_s}$ is equivalent to Type 0A on $S^1$ in the small radius limit, supporting the conjectured endpoint behavior.