Anomalies

Nivedita Deo, Purdue University

Abstract

This thesis studies the structure of local and global anomalies in certain systems and examines the conditions for their cancellation. Gauge anomalies-abelian and non-albelian-antisymmetric tensor, and gravitational anomalies in simple spinor theories with background fields have been analyzed by perturbative methods and local counterterms have been constructed to cancel the anomalies wherever possible. Anomalies occurring in supersymmetric theories in (2 + 1)-dimensions have also been calculated using both perturbative and heat kernel techniques, here again counterterms have been constructed to cancel these parity violating anomalies for certain gauge field configurations. (i) For gauge theories in four dimensions which contain couplings of fermions to a non-abelian antisymmetric tensor field, the contribution of the later to anomalies in the non-abelian chiral Ward identity is computed. It is shown by explicit construction of suitable counterterms that these anomalies can all be cancelled. (ii) The gauge anomalies associated with the gravitational fields in abelian gauge theories can be completely removed provided torsion is nonzero. This is shown by constructing a counterterm associated with the gravitational Goldstone-Wilczek current which cancels the anomalous gravitational contribution to the chiral Ward identity without introducing anomalies in the Lorentz or Einstein Ward identities. (iii) Using perturbative BPHZ renormalization techniques the parity odd part of the effective action has been extracted and explicitly determined for abitrary non-abelian gauge superfields in odd dimensions and shown to be the supersymmetric Chern-Simons secondary topological invariant. (iv) Schwinger's proper time technique is generalized to supersymmetric theories in odd dimensions. The effective action for supersymmetric QED is exactly found for space-time constant superfield. The parity violating anomaly induced in the effective action can be cancelled by adding a local counterterm. (v) A pair of gauge superfield configurations in supersymmetric non-abelian gauge theories in (2 + 1)-dimensions which exhibit the Wu-Yang ambiguity are identified and the effective action computed exactly for one of them, in analogy with (iv). Both configurations give rise to a parity anomaly in the effective action which cannot be removed by the addition of a counterterm.

Degree

Ph.D.

Advisors

Clark, Purdue University.

Subject Area

Particle physics

COinS