Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization

Since the b ghost in the pure spinor formalism is a composite operator depending on non-minimal variables, it is not trivial to impose the Siegel gauge condition b_0 V=0 on BRST-invariant vertex operators. Using the antifield vertex operator V* of ghost-number +2, we show that Siegel gauge unintegrated vertex operators can be constructed as b_0 V* and Siegel gauge integrated vertex operators as \int dz b_{-1} b_0 V*. These Siegel gauge vertex operators depend on the non-minimal variables, so scattering amplitudes involving these operators need to be regularized using the prescription developed previously with Nekrasov. As an example of this regularization prescription, we compute the four-point one-loop amplitude with four Siegel gauge integrated vertex operators. This is the first one-loop computation in the pure spinor formalism that does not require unintegrated vertex operators.Comment: 30 pages latex, added references and comments to Grassi-Vanhove pape

Hilbert space of curved \beta\gamma systems on quadric cones

We clarify the structure of the Hilbert space of curved \beta\gamma systems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.Comment: 45 page

On the b-antighost in the Pure Spinor Quantization of Superstrings

Recently Berkovits has constructed a picture raised, compound field $b_B$ which is used to compute higher loop amplitudes in the pure spinor approach of superstrings. On the other hand, in the twisted and gauge fixed, superembedding approach with $n=2$ world-sheet (w.s.) supersymmetry that reproduces the pure spinor formulation, a field $b$ appears quite naturally as the current of one of the two twisted charges of the w.s. supersymmetry, the other being the BRST charge. In this paper we study the relation between $b$ and $b_B$. We shall show that $bZ$, where $Z$ is a picture raising operator, and $b_B$ belong to the same BRST cohomological class. This result is of importance since it implies that the cumbersome singularity which is present in $b$, is in fact harmless if $b$ is combined with $Z$.Comment: 7 pages, no figures, LaTeX2

Y-formalism and bb ghost in the Non-minimal Pure Spinor Formalism of Superstrings

We present the Y-formalism for the non-minimal pure spinor quantization of superstrings. In the framework of this formalism we compute, at the quantum level, the explicit form of the compound operators involved in the construction of the $b$ ghost, their normal-ordering contributions and the relevant relations among them. We use these results to construct the quantum-mechanical $b$ ghost in the non-minimal pure spinor formalism. Moreover we show that this non-minimal $b$ ghost is cohomologically equivalent to the non-covariant $b$ ghost.Comment: 42 pages, no figure

Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring

Although it is not known how to covariantly quantize the Green-Schwarz (GS) superstring, there exists a semi-light-cone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi-light-cone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring.Comment: 16 pages, JHEP format, fixed typos and added 2 footnote

Die Stadt und der Städtebund in Lykien : Ein historischer Überblick bis zum Jahre 43 n. Chr.

THE SURVEY OF EARLY BYZANTINE SITES IN ÖLÜDENIZ AREA (LYCIA, TURKEY) : THE FIRST PRELIMINARY REPOR

A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring

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 charge $\hat{Q}$, 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 $T(z) = \{\hat{Q}, B(z)\}$, 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.Comment: 38 pages, no figure. Proof of triviality of delta-homology improved and a reference adde