D-brane correlators as solutions of Hirota-Miwa equation

TL;DR

This paper connects D-brane boundary states with integrable systems by showing that tachyon correlators satisfy a generalized Hirota-Miwa equation, revealing new insights into tachyon condensation and D-brane dynamics.

Contribution

It introduces a tachyon field framework that links boundary states to integrable equations and generalizes the Hirota-Miwa equation for systems with two boundaries.

Findings

Correlation functions satisfy the generalized Hirota-Miwa equation.

Coordinates with tachyons are identified as soliton coordinates.

Tachyon condensation effects are analyzed through correlator integration.

Abstract

We present a tachyon field, which simply connects to the calculus of the tachyon condensation. The tachyon field acts on any bare boundary state: the Neumann or the Dirichlet state, and generates the boundary state suggested by S.P. de Alwis, which leads to the correct ratio between D-brane tensions. On the other hand we generalize the Hirota-Miwa equation to the case where there are two boundaries. We show that correlation functions made from only the integrand of the tachyon field satisfy the generalized Hirota-Miwa equation. Using the formulation based on this evidence, we suggest that the coordinates in which there exist tachyons on an unstable D-brane be identified as the soliton coordinates in integrable systems. We also evaluate these correlation functions, which have not yet been integrated, to obtain the local information about the tachyons on unstable D-branes. We further see how these amplitudes are affected through the tachyon condensation by integrating the correlators over the tachyon momenta and taking the on-shell limit.