Abstract
We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi-Yau threefolds. Field-theoretically, these 5d SCFTs descend from 6d mathcal{N} = (1, 0) SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi-Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, how- ever, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.
Highlights
Geometry is a well-established tool in the exploration of the landscape of superconformal field theories (SCFTs)
F-theory compactified on Y gives a 6d SCFT, with flavor symmetry g(F6d) [45, 63, 64], and it is this flavor symmetry, and the remnants of this symmetry that percolate down to 5d, which we will encode in our characterization of the resolution geometries, and in their graphical presentation in terms of combined fiber diagrams (CFDs)
The limit where S collapses to a point — which by construction exists as a partial resolution of the singularity — corresponds to the origin of the Coulomb branch, where the strongly coupled SCFT lives
Summary
Geometry is a well-established tool in the exploration of the landscape of superconformal field theories (SCFTs). F-theory compactified on Y gives a 6d SCFT, with flavor symmetry g(F6d) [45, 63, 64], and it is this flavor symmetry, and the remnants of this symmetry that percolate down to 5d, which we will encode in our characterization of the resolution geometries, and in their graphical presentation in terms of CFDs. There are two approaches to resolve an elliptically fibered Calabi-Yau threefold with non-minimal singularities: one approach, most commonly used in F-theory, is to blow up the non-minimal locus u = v = 0 in the base successively, until the resulting fibration only has minimal Kodaira singularities. We argue that whichever way one chooses to resolve the singularity, it will be key to retain the information about the intersection between the compact surfaces Sj (either from base blow-ups or non-flat resolutions) and the non-compact Cartan divisors (1.2), in order to manifestly encode the flavor symmetries of the 5d SCFTs. In gauge theoretic terms, a resolved geometry corresponds to a point in the extended Coulomb branch of the 5d marginal theory. This agrees with the present geometric analysis, whenever a weakly coupled gauge theory description is available
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
