Geometry, topology and anomalies in Effective Field Theories of condensed matter systems /

Saved in:
Bibliographic Details
Author / Creator:Golkar, Siavash, author.
Ann Arbor : ProQuest Dissertations & Theses, 2015
Description:1 electronic resource (123 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
URL for this record:
Hidden Bibliographic Details
Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Dam T. Son Committee members: Woowon Kang; Kathryn Levin; Savdeep Sethi.
Dissertation Abstracts International, Volume: 77-05(E), Section: B.
Summary:In this thesis we discuss the use of topology and anomalies in the context of effective field theories governing condensed matter systems. After reviewing the related concepts of EFTs, topology and anomalies, we investigate how these concepts can be applied in various condensed matter systems. We first look at the case of anomalous transport in hydrodynamics where the use of anomalies can determine some (but not all) unknown coefficients in the action. We proceed to show that the CVE coefficient that is not fixed by anomalies is not renormalized by interactions and discuss how it can be related to large gauge and diffeomorphism anomalies. We then analyze the EFT governing quantum Hall states in particular we propose a description of relativistic quantum hall which can be applied to graphene. In order to do so we introduce the Euler current, a topological current which is identically conserved in odd dimensions and whose charge is the Euler characteristic of the codimension one surface on which it is calculated. We follow this analysis by considering the case of relativistic superfluids and again see that the Euler current plays a crucial part in implementing topological considerations in the effective field theory. In all these cases, we derive non-trivial predictions for transport coefficients based on the matching EFT parameters to topological considerations.