[Paper Review] Tachyon condensation in boundary string field theory at one loop

K. Bardakçi, Anatoly Konechny|ArXiv.org|May 11, 2001

Black Holes and Theoretical Physics45 references16 citations

TL;DR

This paper computes the one-loop partition function in boundary string field theory (BSFT) for an open string tachyon background with mixed boundary conditions, using both open and closed string representations. It derives one-loop corrections to the tachyon potential and D-brane tensions via analytic continuation of the tachyon mass squared, finding that the imaginary part yields the decay rate of the unstable vacuum and that the corrected D-brane tensions match expected on-shell string theory behavior in the large-tachyon limit.

ABSTRACT

We compute the one-loop partition function for quadratic tachyon background in open string theory. Both closed and open string representations are developed. Using these representations we study the one-loop divergences in the partition function in the presence of the tachyon background. The divergences due to the open and closed string tachyons are treated by analytic continuation in the tachyon mass squared. We pay particular attention to the imaginary part of the analytically continued expressions. The last one gives the decay rate of the unstable vacuum. The dilaton tadpole is also given some partial consideration. The partition function is further used to study corrections to tachyon condensation processes describing brane descent relations. Assuming the boundary string field theory prescription for construction of the string field action via partition function holds at one loop level we study the one-loop corrections to the tachyon potential and to the tensions of lower-dimensional branes.

Motivation & Objective

• To compute the one-loop partition function in boundary string field theory (BSFT) for a quadratic tachyon background with mixed boundary conditions.
• To study one-loop divergences in the presence of open and closed string tachyons using analytic continuation in the tachyon mass squared.
• To derive one-loop corrections to the tachyon potential and to the tensions of lower-dimensional D-branes using the BSFT prescription extended to one loop.
• To assess the stability and coupling behavior of the tachyon condensation process by analyzing the effective action at one-loop order.
• To investigate whether the one-loop corrections preserve the brane descent relations and whether the effective string coupling remains weak during condensation.

Proposed method

• The one-loop partition function is computed in the cylinder picture with time-independent boundary conditions, using BSFT methods to derive the amplitude up to a normalization constant.
• The cylinder is conformally mapped to an annulus, where boundary conditions become modulus-dependent, enabling a dual open and closed string representation.
• The partition function is evaluated using a speculative but consistent extension of the tree-level BSFT prescription to one loop, assuming the same ghost contribution and modular measure as in the conformal case.
• Analytic continuation in the tachyon mass squared is applied to handle divergences, with the imaginary part of the result interpreted as the decay rate of the unstable vacuum.
• The corrected tachyon potential and D-brane tensions are derived from the partition function, with explicit expressions obtained in the limit $ u \to \infty $, corresponding to the full tachyon condensation.

Experimental results

Research questions

• RQ1 How do one-loop corrections modify the tachyon potential in the presence of a quadratic tachyon background in boundary string field theory?
• RQ2 What is the role of analytic continuation in the tachyon mass squared in regulating divergences and extracting the decay rate of the unstable vacuum?
• RQ3 How do the one-loop corrections affect the tensions of lower-dimensional D-branes in the brane descent chain from the D25-brane?
• RQ4 Does the effective string coupling remain weak during tachyon condensation, based on the one-loop partition function?
• RQ5 Are the one-loop corrected D-brane tensions consistent with on-shell string theory expectations in the large-tachyon limit?

Key findings

• The one-loop partition function is computed in both open and closed string representations, with the closed string picture interpreted as a cylinder amplitude with boundary states.
• The imaginary part of the analytically continued partition function yields the decay rate of the unstable vacuum, confirming the expected non-perturbative instability.
• The one-loop corrected tachyon potential is derived via analytic continuation, with the result showing a complex structure consistent with vacuum decay.
• The corrected D-brane tension at one loop is given by $ T_p^{1l} = T_p^{tree}(1 + g\tilde{Z}_p) $, where $ \tilde{Z}_p $ is a modular integral involving the Dedekind eta function.
• In the limit $ u \to \infty $, the one-loop corrected tension for a D0-brane reproduces the expected on-shell result, suggesting consistency with standard string theory.
• The analysis suggests that higher-loop corrections may scale similarly to n-loop partition functions with Dirichlet and Neumann boundaries, implying no significant change in the effective string coupling.