Some mathematical aspects and scattering amplitudes in the pure spinor formalism

Autor(es)

Humberto Gomez Zuñiga

• Tipo de documento: Tese de Doutorado
• Imprenta: São Paulo. 2014-06-11.
• Instituição: Universidade Estadual Paulista (Unesp). Instituto de Física Teórica (IFT). São Paulo
• Data de defesa: 2011-11-10
• Orientador: Nathan Jacob Berkovits; Abraham Hirsz Zimerman

Resumo

First, we give a brief review about the Nekrasov’s paper “Lectures on curved betagamma systems, pure spinors, and anomalies” in order to show the pure spinor formalism is anomaly free when the origin is removed from the pure spinor space. In this way we give a new proposal for the “picture lowering” operators in the minimal pure spinor formalism. We compute the tree level scattering amplitude by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude is 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 three-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. 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. The overall constan factors in the scattering amplitudes are very important because they need to satisfy the unitarity and S-duality conditions [66]. These coefficients have not been computed in the pure spinor formalism due to the difficulty to solve the integrals on the pure spinors space. We compute these integrals by using the non-minimal pure spinor formalism. So, we find the coefficients of the massless one and two-loop four-point amplitude from first principles. Contrasting with the mathematical difficulties in the RNS formalism where unknown normalizations of chiral determinant formulæ force the two-loop coefficient to be... (Complete abstract click electronic access below) (AU)

• Processo FAPESP: 07/54623-8 - Aspectos matematicos de spinores puros.
• Beneficiário: Humberto Gomez Zuñiga
• Modalidade de apoio: Bolsas no Brasil - Doutorado