Explaining the Pure Spinor Formalism for the Superstring

After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b,c) ghosts, together with 12 fermionic constraints. This BRST operator can be obtained by gauge-fixing the Green-Schwarz superstring where the 8 first-class and 8 second-class Green-Schwarz constraints are combined into 12 first-class constraints. Alternatively, the pure spinor BRST operator can be obtained from the RNS formalism by twisting the ten spin-half RNS fermions into five spin-one and five spin-zero fermions, and using the SO(10)/U(5) pure spinor variables to parameterize the different ways of twisting. GSO(-) vertex operators in the pure spinor formalism are constructed using spin fields and picture-changing operators in a manner analogous to Ramond vertex operators in the RNS formalism.Comment: Added two footnotes and references to Baulieu et a

Non-renormalization conditions for four-gluon scattering in supersymmetric string and field theory

The constraints imposed by maximal supersymmetry on multi-loop contributions to the scattering of four open superstrings in the U(N) theory are examined by use of the pure spinor formalism. The double-trace term k^2 t_8(tr F^2)^2 (where k represents an external momentum and F the Yang--Mills field strength) only receives contributions from L<=2 (where L is the loop number) while the single-trace term k^2 t_8(tr F^4) receives contributions from all L. We verified these statements up to L=5, but arguments based on supersymmetry suggest they extend to all L. This explains why the single-trace contributions to low energy maximally supersymmetric Yang--Mills field theory are more divergent in the ultraviolet than the double-trace contributions. We also comment further on the constraints on closed string amplitudes and their implications for ultraviolet divergences in N=8 supergravity.Comment: 25 pages. 2 eps figures. Harvmac format. v2 qualifications regarding comments on closed strings. References adde

Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors

Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.Comment: 10 pages, harvmac TeX. v2: Updated affiliation and Report-no

Light-cone Gauge NSR Strings in Noncritical Dimensions II -- Ramond Sector

Light-cone gauge superstring theory in noncritical dimensions corresponds to a worldsheet theory with nonstandard longitudinal part in the conformal gauge. The longitudinal part of the worldsheet theory is a superconformal field theory called X^{\pm} CFT. We show that the X^{\pm} CFT combined with the super-reparametrization ghost system can be described by free variables. It is possible to express the correlation functions in terms of these free variables. Bosonizing the free variables, we construct the spin fields and BRST invariant vertex operators for the Ramond sector in the conformal gauge formulation. By using these vertex operators, we can rewrite the tree amplitudes of the noncritical light-cone gauge string field theory, with external lines in the (R,R) sector as well as those in the (NS,NS) sector, in a BRST invariant way.Comment: 33 pages; v2: minor modification

Estimation of GRB detection by FiberGLAST

FiberGLAST is one of several instrument concepts being developed for possible inclusion as the primary Gamma-ray Large Area Space Telescope (GLAST) instrument. The predicted FiberGLAST effective area is more than 12,000 cm2 for energies between 30 MeV and 300 GeV, with a field of view that is essentially flat from 0°–80°. The detector will achieve a sensitivity more than 10 times that of EGRET. We present results of simulations that illustrate the sensitivity of FiberGLAST for the detection of gamma-ray bursts