[Paper Review] Brane - Anti-Brane Forces

Tom Banks, Leonard Susskind|ArXiv.org|Nov 27, 1995

Energetic Materials and Combustion48 citations

TL;DR

This paper investigates the quantum mechanical forces between D-branes of opposite charge in type IIA string theory, showing that the Born-Oppenheimer approximation breaks down at distances near the string scale due to a complex potential signaling inelastic processes. The key result is the emergence of a tachyonic instability in the open string sector when branes approach within ~√α′, leading to tachyon condensation and annihilation into closed strings, with implications for black hole formation and entropy in string theory.

ABSTRACT

The force between like sign BPS saturated objects generally vanishes. This is a reflection of the fact that BPS states are really massless uncharged particles with nonvanishing momenta in compactified directions. Two like sign BPS objects with zero relative velocity can be viewed as a boosted state of two neutral massless particles in a state of vanishing relative motion. By contrast two unlike sign BPS particles may be thought of as colliding objects moving in opposite directions in compact space. This leads to complicated interactions which are totally intractable at present. We illustrate this by considering the potential between opposite sign zero-D- branes .

Motivation & Objective

• To understand the nature of forces between oppositely charged D-branes, especially when BPS saturation no longer protects against interactions.
• To analyze the breakdown of the Born-Oppenheimer approximation in brane-antibrane systems at short distances.
• To investigate the emergence of inelastic processes and tachyon condensation as a precursor to black hole formation.
• To explore the connection between brane-antibrane annihilation and thermodynamic entropy in string theory.

Proposed method

• Calculates the potential between opposite-sign zero-branes using open string one-loop annulus diagrams in the type IIA string theory framework.
• Evaluates the partition function with boundary conditions corresponding to two D-branes, distinguishing contributions from NS-NS and R-R closed string exchanges.
• Identifies the breakdown of cancellation between NS-NS and R-R terms when charges are opposite, leading to a non-vanishing potential.
• Analyzes the resulting potential and force integrals, showing divergence and complex behavior when the squared distance Y² < 2π².
• Introduces a tachyon field T in the effective potential V = ZT² + Cg²T⁴, where Z becomes negative at short distances.
• Uses the tachyon effective action to model condensation, with C < 0 indicating a discontinuous transition and metastability.

Experimental results

Research questions

• RQ1 What happens to the potential between oppositely charged D-branes when the Born-Oppenheimer approximation is applied at short distances?
• RQ2 Why does the potential become complex and divergent for Y² < 2π², and what does this imply physically?
• RQ3 How does the tachyon field in the open string sector drive the annihilation of brane-antibrane pairs?
• RQ4 Can the tachyon condensation process be linked to black hole formation or entropy in string theory?
• RQ5 What is the role of degeneracy and tunnelling in the two-fold ground state of the tachyon condensate?

Key findings

• The potential between opposite-sign zero-branes becomes complex and divergent when Y² < 2π², signaling the onset of inelastic processes.
• The force diverges as 1/√Z, where Z ∝ (Y²/(2π²) − 1), indicating a singularity at short distances.
• The system develops a tachyonic instability when Z < 0, corresponding to the lightest open string connecting the branes becoming tachyonic.
• The tachyon effective potential V = ZT² + Cg²T⁴ has C < 0, implying a discontinuous condensate formation at T ∼ 1/g.
• The condensate involves ∼1/g² open strings, suggesting a transition to a new vacuum state via annihilation into closed strings.
• The two-fold degeneracy in the tachyon sign leads to exponentially suppressed tunnelling, implying macroscopic irreversibility and a possible origin of entropy in black hole formation.