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Geometric classification of 4d rank-1 N=2 superconformal field theories

Lotito, Matteo
http://orcid.org/0000-0003-3052-203X
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1530880263562131

Abstract Details

2018, PhD, University of Cincinnati, Arts and Sciences: Physics.
In this thesis work, we present a systematic classification of four dimensional rank-1 N=2 superconformal field theories (SCFTs). The analysis is based on extracting the low energy properties of N=2 SCFTs through the study of the structure of their Coulomb branch geometries. The original work of Seiberg and Witten provided the key to interpret features of $\cN=2$ theories in terms of geometrical objects. Generalizing from that seminal work, we show how a systematic description of rank-1 N=2 SCFTs is possible. An important property to consider is that a scale invariant Coulomb Branch geometry does not fully characterize a theory; we have to introduce a set of deformations, that still preserve the N=2 supersymmetry structure, together with consistency conditions for them, to distinguish theories sharing the same scale invariant behavior. The main outcome of our study is to provide a classification of the flavor algebras for the theories corresponding to the geometries we study. We carry this out in two ways. The first, called the algebraic approach, directly extends the work of Seiberg and Witten (and subsequent research). The second, topological approach, is a field theoretic extension of work originated in the string theory literature. In either case, the preexisting research provided only a partial answer to our problem, essentially describing only the subset of all the possible geometries that we call the ``maximal deformations''. Our construction is to be contrasted and in fact complements the conformal bootstrap framework, which instead of studying the low energy properties of these theories relies on the constraints of the full conformal symmetry of the microscopic theory.
Philip Argyres, Ph.D. (Committee Chair)
Carlos Bolech, Ph.D. (Committee Member)
Alexandre Sousa, Ph.D. (Committee Member)
L.C.R. Wijewardhana, Ph.D. (Committee Member)
362 p.
Physics
supersymmetric gauge theory; conformal field theory; extended supersymmetry; conformal and w symmetry; moduli space

Recommended Citations

Citations

  • Lotito, M. (2018). Geometric classification of 4d rank-1 N=2 superconformal field theories [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1530880263562131

    APA Style (7th edition)

  • Lotito, Matteo. Geometric classification of 4d rank-1 N=2 superconformal field theories. 2018. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1530880263562131.

    MLA Style (8th edition)

  • Lotito, Matteo. "Geometric classification of 4d rank-1 N=2 superconformal field theories." Doctoral dissertation, University of Cincinnati, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1530880263562131

    Chicago Manual of Style (17th edition)

ucin1530880263562131
408
© 2018, some rights reserved.Creative Commons License Geometric classification of 4d rank-1 N=2 superconformal field theories by Matteo Lotito is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.