A new first class algebra, homological perturbation and extension of pure spinor formalism for superstring

Abstract

Based on a novel first class algebra, we develop an extension of the pure spinor (PS) formalism of Berkovits, in which the PS constraints are removed. By using the homological perturbation theory in an essential way, the BRST-like charge Q of the conventional PS formalism is promoted to a bona fide nilpotent chargeQ, the cohomology of which is equivalent to the constrained cohomology of Q. This construction requires only a minimum number (five) of additional fermionic ghost-antighost pairs and the vertex operators for the massless modes of open string are obtained in a systematic way. Furthermore, we present a simple composite "b-ghost" field B(z) which realizes the important relation T (z) = {Q, B(z)}, with T (z) the Virasoro operator, and apply it to facilitate the construction of the integrated vertex. The present formalism utilizes U(5) parametrization and the manifest Lorentz covariance is yet to be achieved. †

On D-brane boundary state analysis in pure spinor formalism

“…They can be shown to give zero inner product with the correct form of the boundary state, 16) which are also expected results.…”

“…Our approach will 2 Attempts have been made in [14] to understand the origin of this approach. 3 Extensions of the present framework by relaxing this constraint have been considered in [15,16]. 4 See, for example, [21] for reviews on this subject in NSR formalism.…”

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

“…22 And when λ α (v) goes around the R th B-cycle, the change in the correlation function can be cancelled by shifting the zero mode of J R .…”

Covariant map between Ramond-Neveu-Schwarz and pure spinor formalisms for the superstring

“…The definition of (1.8) for the unconstrained Λ α might be useful for understanding the relation with "extended" versions of the pure spinor formalism such as [20][21][22][23] in which the spinor ghosts were unconstrained. After defining Γ m and Γ m as in (1.5), the RNS γ ghost only appears in even powers so it is convenient to define a new ghost variable γ ≡ (γ) 2 .…”