[Paper Review] Remarks on Tachyon Condensation in Superstring Field Theory

David Kutasov, Marcos Mariño+1 more|ArXiv.org|Oct 13, 2000

Black Holes and Theoretical Physics28 references150 citations

TL;DR

This paper generalizes boundary string field theory (BSFT) to superstring theory, demonstrating that tachyon condensation on unstable D-branes in Type II superstrings can be efficiently described using a worldsheet RG approach. The key result is that the BSFT action correctly reproduces the descent relations for D-brane tensions, including the factor of √2 for non-BPS branes, and confirms the RR charge distribution on the resulting D8-brane via one-point functions.

ABSTRACT

We generalize recent results on tachyon condensation in boundary string field theory to the superstring.

Motivation & Objective

• To extend the successful description of tachyon condensation in bosonic string field theory to the superstring case.
• To investigate whether BSFT provides an efficient framework for studying tachyon condensation in superstring theory, analogous to its success in the bosonic case.
• To verify that the resulting tachyon profiles correctly reproduce known descent relations for D-brane tensions in superstring theory.
• To examine the role of RR charges in the tachyon condensation process using worldsheet techniques in BSFT.
• To explore the stability and structure of the final state after tachyon condensation, particularly the emergence of stable D8-branes.

Proposed method

• Formulate a superstring version of boundary string field theory (BSFT) by extending the action to include worldsheet supersymmetry, using the boundary entropy as the spacetime action.
• Define the spacetime action as $ S = Z - \frac{dZ}{d\log|x|} $, where $ Z $ is the disk partition function, to eliminate divergences and ensure criticality at fixed points.
• Use the Callan-Symanzik equation to relate the action to the worldsheet RG flow, ensuring the action decreases monotonically along the flow.
• Construct the tachyon profile as a linear function of spacetime coordinates, $ T = uX^1 $, which describes a codimension-one kink and corresponds to a D8-brane.
• Compute the one-point function of the RR vertex operator in the $(-3/2, -1/2)$ picture to determine the RR charge distribution on the D8-brane.
• Generalize the formalism to $ D\bar{D} $ systems by using a matrix tachyon profile $ \begin{pmatrix} 0 & T \\ T^\dagger & 0 \end{pmatrix} $.

Experimental results

Research questions

• RQ1 Can the BSFT formalism, successful in the bosonic string, be extended to describe tachyon condensation in the superstring?
• RQ2 Does the BSFT action correctly reproduce the known descent relations for D-brane tensions in Type II superstrings?
• RQ3 How is the RR charge of the final D-brane state encoded in the worldsheet path integral within the BSFT framework?
• RQ4 Why does the final state after tachyon condensation in the superstring case correspond to a stable D8-brane, unlike in the bosonic case?
• RQ5 What is the role of worldsheet supersymmetry in resolving the divergences and criticality issues present in the bosonic BSFT?

Key findings

• The BSFT action correctly reproduces the tension of the D8-brane resulting from tachyon condensation, yielding $ T_8 = \frac{2\pi\sqrt{\alpha^\prime}}{\sqrt{2}} T_9 $, matching the expected value.
• The descent relation for non-BPS D-branes is reproduced as $ \frac{T_{9-n}}{2^{[n/2]} T_9} = (\pi\sqrt{2\alpha^\prime})^n $, with a factor of $ \frac{1}{\sqrt{2}} $ for odd $ n $, consistent with known results.
• The RR charge of the D8-brane is found to be distributed equally on both sides of the brane, as expected from spacetime arguments, via the one-point function computation.
• The tachyon profile $ T = uX^1 $ leads to a stable D8-brane because the resulting worldsheet theory is free and the kink is codimension one, preserving spacetime Poincaré invariance.
• The BSFT formalism successfully avoids the divergences of the naive partition function by using the boundary entropy definition $ S = Z - \frac{dZ}{d\log|x|} $, which is finite and monotonic.
• The method confirms that tachyon condensation in the superstring leads to a stable final state, unlike in the bosonic case where further decay is possible.