Abstract
After constructing a simplified four-dimensional version of the b ghost, topological multiloop amplitudes in type II superstring theory compactified on a six-dimensional orbifold are computed using the non-minimal pure spinor formalism. These pure spinor amplitude computations preserve manifest N = 2 D = 4 supersymmetry and, unlike the analogous topological multiloop amplitude computations using the hybrid formalism, can be extended to non-topological amplitudes.
Highlights
This hybrid formalism involves Green-Schwarz-like variables for the D = 4 superspace, RNS-like variables for the internal six-dimensional compactification, and left- and rightmoving chiral bosons, ρ and ρ
After including non-minimal variables which decouple from the BRST cohomology and constructing a composite b ghost, this pure spinor formalism [7] has been used in a flat D = 10 background to compute multiloop superstring amplitudes up to three loops
The pure spinor vertex operators depend on all 16 θα and 16 θα worldsheet variables, the restriction to patches where λα = 0 and the construction of a four-dimensional version of the b ghost simplify the computations
Summary
The pure spinor λα, whose components have conformal weight 0, enters into the worldsheet action together with its conjugate momentum wα of opposite chirality, which has components of conformal weight +1. This variable wα has eleven degrees of freedom because the pure spinor constraint allows for the gauge invariance δwα = Λm(γmλ)α. The massless closed string vertex operator is a left-right product and has the form V = λαλβAαβ V = λαλβAα β for type IIB (IIA). Equations of motion and gauge invariance come from cohomology requirements on both left- and right-moving sectors by means of BRST charges Q and Q, and describe linearized type IIB (IIA) supergravity in ten dimensions. This pure spinor construction will be adapted to the case of type II superstrings compactified on an orbifold to four-dimensional Minkowski spacetime
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