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Title: The Schur index of 4d N 2 superconformal eld theories
Author: Bourdier, Jun
ISNI:       0000 0004 6058 145X
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2017
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We study in this thesis the superconformal index of 4-dimensional N 2 SUpNq gauge eld theories on S1 S3. We focus in particular on a reduced version of the index, known as the Schur index, with only one fugacity q for the space-time symmetries. We start by studying circular quiver gauge theories which can be diagrammatically represented in a way reminiscent of A^ Dynkin diagrams. The Schur index of these theories is usually given in terms of a complex matrix model involving various elliptic functions. We use an elliptic determinant identity to simplify the integrand and express it in terms of determinants, allowing us to rewrite the whole index as a weighted sum over partition functions of free Fermi gases living on a circle. Each partition function is then studied in the grand canonical ensemble and we nd exact compact expressions for the analogue of the grand partition function which we dene as the grand index. For short quivers with only one or two nodes we are able to analytically deduce the Schur index exaclty as a q-series, and for small values of N we are able to express it in terms of the complete elliptic integrals of the rst and second kind. For longer quivers, we are able to extract the Schur index in the large N limit, up to non-perturbative corrections. We also investigate another class of theories, namely ^D-type quivers, for which we are able to apply the same techniques. We obtain the grand index as well as a simple and compact expression for its leading term in the large chemical potential limit. This thesis also contains a detailed review of the superconformal index, a comparison of our results with some other previously known expressions for the Schur index obtained through other formalisms, as well as various technical appendices.
Supervisor: Drukker, Nadav ; Gromov, Nikolay Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available