Studies on Strings and Anomalies.
Abstract
This thesis involves studies on two different but closely related subjects, namely, strings and anomalies. The string theories offer the hope of unifying all known fundamental interactions. And the only string theories which are consistent, i.e., free of anomalies, are the superstring theories in ten dimensional space-time with unique internal symmetry groups. After a brief survey of the properties of the various string theories and anomalies, we study in detail the anomaly-free string theories in the compactified dimensions. The general group-theoretic argument to the dimensional reduction and the definition of the compactification condition of the string theories are given. It is shown by explicit calculations that the E_ 8 times E_ 8 and the SO(16) times SO(16) heterotic string theories, remain anomaly -free in every compactified even dimension only if the proper compactification condition is satisfied. Furthermore the global anomaly of the SO(16) times SO(16) heterotic string is derived and possible compactified manifolds are discussed. Finally, we argue that if the Green-Schwarz mechanism makes a theory anomaly-free in 10-dimension, then it remains anomaly-free in 8 and 4 dimensions and for the theory to be anomaly-free in 6-dimension a consistent constraint on the 10-dimensional spin 3/2 fields is needed. The index theorem which is closely related to the anomaly is discussed. We consider the generalized Dirac operator with torsion. It is proved rigorously that the index theorem is independent of torsion. We also calculate the Witten index in superspace. We show that the generalized Witten index in superspace has a close relationship with the superspace Schwinger-Dewitt heat kernel. Using the generalized Witten index, the superanomaly in Yang-Mills and gravitational backgrounds are evaluated. Furthermore, it is shown how to evaluate effectively the 3-dimensional parity anomaly by applying the superspace Schwinger-Dewitt heat kernel method. Finally, we show that the {rm (4k - 1)}-dimensional gravity theories in Euclidean space is anomalous.
- Publication:
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Ph.D. Thesis
- Pub Date:
- September 1987
- Bibcode:
- 1987PhDT........91K
- Keywords:
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- Physics: Elementary Particles and High Energy