In this work, a particular BRST-exact class of deformations of the b ghost in the non-minimal pure spinor formalism is investigated and the impact of this construction in the $\mathcal{N}=2$ $\hat{c}=3$ topological string algebra is analysed. As an example, a subclass of deformations is explicitly shown, where the U(1) current appears in a conventional form, involving only the ghost number currents. Furthermore, a c ghost like composite field is introduced, but with an unusual construction.
The OPE between the composite $b$ ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The vanishing of the double pole singularity is Lorentz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator.
The construction of the ghost number zero and one vertex operators for the 11D pure spinor superparticle will be revisited. In this sense, an alternative way of defining the ghost number one vertex operator will be given after introducing a ghost number -2 operator made out of physical operators defined on the 11D non-minimal pure spinor superspace. This procedure will make explicit and transparent the relation between the ghost number three and one vertex operators. In addition, using a non-Lorentz covariant b-ghost, ghost number zero and two vertex operators satisfying standard descent equat…
The 11D pure spinor ghost number zero vertex operator
Uppsala University（乌普萨拉大学）；Chalmers University of Technology（查尔姆斯理工大学）；University of Gothenburg（哥德堡大学）；ICTP South American Institute for Fundamental Research Instituto de Física Teórica, UNESP-Universidade Estadual Paulista（国际理论物理研究所南美基础研究院理论物理研究所，圣保罗州立大学）；Center for Quantum Mathematics and Physics (QMAP) Department of Physics & Astronomy, University of California, Davis（加州大学戴维斯分校量子数学与物理中心（QMAP）物理与天文系）；Instituto Gallego de Física de Altas Energías (IGFAE)（加利西亚高能物理研究所）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）
The $b$ ghost, or $b$ operator, used for fixing Siegel gauge in the pure spinor superfield formalism, is a composite operator of negative ghost number, satisfying $\{q,b\}=\square$, where $q$ is the pure spinor differential (BRST operator). It is traditionally constructed using non-minimal variables. However, since all cohomology has minimal representatives, it seems likely that there should be versions of physically meaningful operators, also with negative ghost number, using only minimal variables. The purpose of this letter is to demonstrate that this statement holds by providing a concrete…
In this Thesis we study first- and second-quantized approaches describing $D=11$ supergravity using pure spinor variables. We introduce the so-called $D=11$ pure spinor superparticle through BRST cohomology arguments starting from the semi-light-cone gauge $D=11$ Brink-Schwarz-like superparticle. After performing a light-cone gauge analysis of the pure spinor BRST cohomology at ghost number three, we find the linearized equations of motion of $D=11$ supergravity in $D=9$ superspace. In addition, we construct a BRST-closed, ghost number one vertex operator made out of worldline fields and $D=11…
We perform the quantisation of antisymmetric tensor-spinors (fermionic $p$-forms) $ψ^α_{μ_1 \dots μ_p}$ using the Batalin-Vilkovisky field-antifield formalism. Just as for the gravitino ($p=1$), an extra propagating Nielsen-Kallosh ghost appears in quadratic gauges containing a differential operator. The appearance of this `third ghost' is described within the BV formalism for arbitrary reducible gauge theories. We then use the resulting spectrum of ghosts and the Atiyah-Singer index theorem to compute gravitational anomalies.
Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
由于纯旋量形式中的b鬼是一个依赖于非极小变量的复合算子，因此将Siegel规范条件b_0 V=0强加于BRST不变顶点算子上是很重要的。利用虚数为+2的反场顶点算符V ~*，我们证明了Siegel规范非积分顶点算符可以构造为b_0 V ~*，Siegel规范积分顶点算符可以构造为\int dz b_{-1} b_0 V ~*.这些Siegel规范顶点算子依赖于非最小变量，因此涉及这些算子的散射振幅需要使用Nekrasov先前开发的处方进行正则化。作为这种正则化处方的一个例子，我们计算四点单圈振幅与四个西格尔规范集成顶点运营商。这是纯旋量形式主义中第一个不需要不可积顶点算子的单循环计算。
Using the pure spinor master action for 10D super-Yang-Mills in the gauge $b_{0}V = QΞ$, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested $b$-ghost operators, and show that the Siegel gauge condition $b_{0}V = 0$ gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.
