Correlators of Ramond-Neveu-Schwarz Fields in String Theory
Jul 15, 2011189 pages
Supervisors:
Thesis: PhD - ,
- Munich U.
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Abstract:
In this thesis we provide calculational tools in order to calculate scat tering amplitudes in string theory at tree- and loop-level. In particular, we discuss the calculation of correlation functions consisting of Ramond–Neveu–Schwarz fields in four, six, eight and ten space-time dimensions and calculate the amplitude involving two gauge fields and fo ur gauginos at tree-level. Multi-parton superstring amplitudes are of considerable theoretic al interest in the frame-work of a full-fledged superstring theory and of phenomen ological interest in describ- ing corrections to four-dimensional scattering processes. The N eveu–Schwarz fermions and Ramond spin fields enter the scattering amplitudes through vertex operators of bosonic and fermionic string states and determine the Lorentz structure of the total amplitude. Due to their interacting nature their correlators cannot be evalua ted using Wick’s theorem but must be calculated from first principles. At tree-level such correlation functions can be determined by ana lyzing their Lorentz and singularity structure. In four space-time dimensions we show h ow to calculate Ramond– Neveu–Schwarz correlators with any number of fields. This method is based on factorizing the expressions into correlators involving only left- or right-hande d spin fields and calcu- lating these functions. This factorization property does not hold in higher dimensions. Nevertheless, we are able to calculate certain classes of correlato rs with arbitrary many fields. Additionally, in eight dimensions we can profit from SO (8) triality to derive further tree-level correlation functions. Ramond–Neveu–Schwarz correlators at loop-level can be evaluat ed by re-expressing the fermions and spin fields in terms of SO (2) spin system operators. Using this method we present expressions for all correlators up to six-point level and s how in addition results for certain classes of correlators with any number of fields. Our fin dings hold for string scattering at arbitrary loop order. To complement the discussion we calculate the tree-level amplitude o f two gauge fields and four gauginos for string compactifications to four dimensions a nd give its field theory limit. This open string amplitude is of particular interest because it can be related to an open-closed amplitude involving gauge fields and bulk moduli. In this way the mapping between the open and the open-closed sector can be studied in gre at detail and brane-bulk couplings can be determined in terms of open string couplings- scattering amplitude
- string model
- tree approximation
- correlation function
- Ramond
- gaugino
- triality
- SO(8)
- string: scattering
- string: compactification
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