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On the Classification of Rank-1 Four-dimensional N=2 Superconformal Field Theories by Seiberg-Witten Geometry

Lu, Yongchao
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1505211291169085

Abstract Details

2017, PhD, University of Cincinnati, Arts and Sciences: Physics.
We develop a systematic approach to the classification of four dimensional N = 2 supercon- formal field theories (SCFTs) with a one dimensional moduli space of Coulomb vacua with planar topology, equivalently, of four dimensional N = 2 SCFTs with rank one freely gen- erated Coulomb branch (CB) chiral rings. The geometric structure of the Coulomb branch encodes ultraviolet conformal field theory data: the relevant mass deformations of the UV N = 2 SCFTs are mapped to the complex deformations of singular Coulomb branch ge- ometries. Our results go beyond the standard lore of the A-D-E classification, and a richer pattern of flavor symmetries is revealed corresponding to different deformations. We have constructed explicit Seiberg-Witten (SW) curves and one-forms for each pos- sible regular deformation of the CB geometry. Further physical consistency conditions are obtained by considering N = 2 RG flows, and certain SW geometries are ruled out by our conjecture about the absence of dangerously irrelevant operators in N = 2 field theories. Along the way, we have discovered a full list of new rank-1 N = 2 SCFTs, notably including the rank-1 N = 3 SCFTs constructed via the S-fold construction in Type IIB string theory. The structure of the Higgs branch and enhanced Coulomb branches of these N = 2 SCFTs is also examined in terms of N = 2 chiral ring relations and N = 2 S-dualities. The conformal and flavor central charges are computed by a refined version of Shapere and Tachikawa’s topological twisting argument. We also initiate a systematic study of rank-1 SCFTs with CB chiral rings satisfying non-trivial operator product expansion relations, and the SW geometry of the corresponding non-planar CBs. The main result of our study is that (rank-1) SCFTs with non-freely generated CB chiral rings when deformed by relevant deformations, always flow to theories with non-freely generated CB rings. This implies that if they exist, they must thus form a distinct subset under RG flows. We also find many interesting characteristic properties that these putative theories satisfy which may be helpful in proving or disproving their existence using other methods.
Philip Argyres, Ph.D. (Committee Chair)
Colin Bischoff, Ph.D. (Committee Member)
L.C.R. Wijewardhana, Ph.D. (Committee Member)
Jure Zupan, Ph.D. (Committee Member)
155 p.
Theoretical Physics
SCFTs; Coulomb branch; Seiberg-Witten geometry; Planar CB; Non Planar CB

Recommended Citations

Citations

  • Lu, Y. (2017). On the Classification of Rank-1 Four-dimensional N=2 Superconformal Field Theories by Seiberg-Witten Geometry [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1505211291169085

    APA Style (7th edition)

  • Lu, Yongchao. On the Classification of Rank-1 Four-dimensional N=2 Superconformal Field Theories by Seiberg-Witten Geometry. 2017. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1505211291169085.

    MLA Style (8th edition)

  • Lu, Yongchao. "On the Classification of Rank-1 Four-dimensional N=2 Superconformal Field Theories by Seiberg-Witten Geometry." Doctoral dissertation, University of Cincinnati, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1505211291169085

    Chicago Manual of Style (17th edition)

ucin1505211291169085
381
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This open access ETD is published by University of Cincinnati and OhioLINK.