A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism

Humberto Gomez; Oscar A. Bedoya

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A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism

Oscar A. Bedoya, Humberto Gomez

High Energy Physics - Theory · Submitted 7 Jun 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

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arXiv ID1106.1253 (version 2)

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CitationHumberto Gomez, Oscar A. Bedoya. "A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism." arXiv:1106.1253 (2011). https://pith.science/paper/GOISLXXC

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.83 · mentions code or data availability 0.02.

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Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green's function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral.	contribution 0.56	0.95	0.36	asserted 1.00
s1	The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism.	interpretation 0.40	0.88	0.15	asserted 0.93
s2	The natural language for relating these formalisms is the Cech-Dolbeault isomorphism.	background 0.34	0.25	0.07	asserted 1.00
s3	Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space.	method 0.65	0.74	0.09	asserted 1.00
s4	Also, the Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states.	contribution 0.45	0.81	0.13	asserted 1.00
s5	We also relate the Green's function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders.	contribution 0.63	0.88	0.07	asserted 0.97
s6	In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.	result 0.91	0.93	0.46	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.59 · evidence from proof or derivation 1.00.

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S sections
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The paper

Original abstract

Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green's function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

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2 arXiv papers cite this in 2 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

We show however by explicit tree-level and one-loop computations that the picture changing operators are not BRST closed inside correlators and the amplitudes do depend on these constant tensors.

Decoupling of unphysical states in the minimal pure spinor formalism I · 0.94

What it cites · 65 sentences without a confident label

Contests 4 papers

Although in [ref] it was argued that the scattering amplitude was independent of the constant spinors $C_^I$, it was later found in [ref] that indeed the amplitude depends on the choice of $C_^I$ and also that $Q$ exact states do not decouple.

Decoupling of unphysical states in the minimal pure spinor formalism I · Review of Minimal Pure Spinor Formalism · contest 0.87
Although in [ref] it was argued that the scattering amplitude was independent of the constant spinors $C_^I$, it was later found in [ref] that indeed the amplitude depends on the choice of $C_^I$ and also that $Q$ exact states do not decouple.

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring · Review of Minimal Pure Spinor Formalism · contest 0.87
From the analysis above we can conclude that for the tree level scattering amplitudes, the naive existence of the homotopy operator [ref] [ref] given by [equation] which by definition satisfies [equation] for $V_1V_2V_3$ unintegrated vertex operators and $U_1...U_N-3$ integrated vertex operators, is not allowed because [equation] is not a global function on $PS∖{0}$.

Pure Spinor Formalism as an N=2 Topological String · BRST Invariance · contest 0.76

Uses the method or tool of 1 paper

The most useful regulator in the non-minimal pure spinor formalism for computing the tree level scattering amplitude is [equation] as given in [ref] , where $r_$ is a spinor such that $r_(^m)^_=̱0$.

Pure Spinor Formalism as an N=2 Topological String · A Particular Regulator · 0.89

Uses data or values from 1 paper

So using ([ref]), ([ref]), ([ref]) and ([ref]) we can conclude [equation] As computed in [ref] , the degree of the projective pure spinor space is 12.

One-loop Superstring Amplitude From Integrals on Pure Spinors Space · The Projective Pure Spinor Degree · 0.95

Compares with 3 papers

Choosing $= =̱ = +$ we obtain [equation] which is exactly the same answer found by Skenderis and Hoogeveen in [ref] , as in their case, it is not Lorentz invariant.

Decoupling of unphysical states in the minimal pure spinor formalism I · Some Examples for the Constant Spinors $C^I _α$ · 1.00
In this section we will show that the result found there, given by the integral ([ref]), is the same found by Berkovits and Cherkis in [ref] .

Higher-Dimensional Twistor Transforms using Pure Spinors · Relation with Twistor Space · 0.95
In contrast with the minimal formalism, in the non-minimal formulation it is possible to compute tree level amplitude with all the vertex operators unintegrated [ref] .

Pure Spinor Formalism as an N=2 Topological String · Conclusions · 0.89

Cites as support 1 paper

Furthermore, as was shown explicitly by tree and one-loop computations, given the distributional definition of the PCO's $Y_Old^I$, the scattering amplitudes depends on the constant spinors $C^I$; so for some choices of these $C^I$'s, the theory is non-Lorentz invariant and the unphysical states do not decouple [ref] .

Decoupling of unphysical states in the minimal pure spinor formalism I · Introduction · 0.96

Cites as background 8 papers

The prescription for computing multiloop amplitudes was given in [ref] , where as in the RNS formalism, it was necessary to introduce picture changing operators (PCO's) in order to absorb the zero-modes of the pure spinor variables.

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring · Introduction · 0.94
Later on, by introducing a set of non-minimal variables $ł̅_$ and $r_$, an equivalent prescription for computing scattering amplitudes was formulated in [ref] and [ref] .

Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism · Introduction · 0.92
When $=0$ then $ł^=0$, but $ł̃^$ can take any value in the projective pure spinor space, i.e $SO(10)/U(5)$, also known as the twistor space [ref] .

Higher-Dimensional Twistor Transforms using Pure Spinors · Contours for the Amplitude in the Projective Pure Spinor Coordinates · 0.83

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