DDF Construction and D-Brane Boundary States in Pure Spinor Formalism

TL;DR

This paper constructs DDF states and boundary states for non-BPS D-branes in pure spinor formalism, establishing a correspondence with light-cone Green-Schwarz formalism and enabling calculations of cylinder diagrams with open-closed duality.

Contribution

It provides explicit DDF state construction in pure spinor formalism for both open and closed strings, linking covariant and light-cone formalisms.

Findings

DDF states are explicitly constructed and proven valid.

Boundary states match light-cone Green-Schwarz form.

Framework enables cylinder diagram computations with duality.

Abstract

Open string boundary conditions for non-BPS D-branes in type II string theories discussed in hep-th/0505157 give rise to two sectors with integer (R sector) and half-integer (NS sector) modes for the combined fermionic matter and bosonic ghost variables in pure spinor formalism. Exploiting the manifest supersymmetry of the formalism we explicitly construct the DDF (Del Giudice, Di Vecchia, Fubini) states in both the sectors which are in one-to-one correspondence with the states in light-cone Green-Schwarz formalism. We also give a proof of validity of this construction. A similar construction in the closed string sector enables us to define a physical Hilbert space in pure spinor formalism which is used to project the covariant boundary states of both the BPS and non-BPS instantonic D-branes. These projected boundary states take exactly the same form as those found in light-cone Green-Schwarz formalism and are suitable for computing the cylinder diagram with manifest open-closed duality.