446 research outputs found
On the b-antighost in the Pure Spinor Quantization of Superstrings
Recently Berkovits has constructed a picture raised, compound field
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 world-sheet (w.s.) supersymmetry that reproduces the pure
spinor formulation, a field 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 and . We shall
show that , where is a picture raising operator, and belong to
the same BRST cohomological class. This result is of importance since it
implies that the cumbersome singularity which is present in , is in fact
harmless if is combined with .Comment: 7 pages, no figures, LaTeX2
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
Y-formalism and 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 ghost, their normal-ordering contributions and the relevant
relations among them. We use these results to construct the quantum-mechanical
ghost in the non-minimal pure spinor formalism. Moreover we show that this
non-minimal ghost is cohomologically equivalent to the non-covariant
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
Worldline Approach of Topological BF Theory
We present a worldline description of topological non-abelian BF theory in
arbitrary space-time dimensions. It is shown that starting with a trivial
classical action defined on the worldline, the BRST cohomology has a natural
representation as the sum of the de Rham cohomology. Based on this observation,
we construct a second-quantized action of the BF theory. Interestingly enough,
this theory naturally gives us a minimal solution to the Batalin-Vilkovisky
master equation of the BF theory. Our formalism sheds some light not only on an
interplay between the Witten-type and the Schwarz-type topological quantum
field theories but also on the role of the Batalin-Vilkovisky antifields and
ghosts as geometrical and elementary objects.Comment: 12 pages, no figures, references adde
Die Stadt und der Städtebund in Lykien : Ein historischer Überblick bis zum Jahre 43 n. Chr.
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D=11 supergravity with manifest supersymmetry
The complete supersymmetric action for eleven-dimensional supergravity is
presented. The action is polynomial in the scalar fermionic pure spinor
superfield, and contains only a minor modification to the recently proposed
three-point coupling.Comment: 14 pp., plain te
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