On the classification of 5 d SCFTs
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Springer
Received: June 25, 2020 Accepted: August 4, 2020 Published: September 1, 2020
Lakshya Bhardwaj Department of Physics, Harvard University, 17 Oxford St, Cambridge, MA 02138, U.S.A.
E-mail: [email protected] Abstract: We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5d KK theories. Keywords: Conformal Field Models in String Theory, Field Theories in Higher Dimensions, Conformal Field Theory, M-Theory ArXiv ePrint: 1909.09635
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)007
JHEP09(2020)007
On the classification of 5d SCFTs
Contents 1
2 Rank one 2.1 M = 9 2.2 M = 2
2 5 8
3 Rank two 3.1 M = 11 3.2 M = 10 3.3 M = 7 3.4 M = 4 3.5 M = 3 3.6 M = 2 3.7 M = 1
11 14 20 22 23 25 26 29
4 Rank three 4.1 M = 13 4.2 M = 12 4.3 M = 11 4.4 M = 10 4.5 M = 8 4.6 M = 6 4.7 M = 5 4.8 M = 4 4.9 M = 3 4.10 M = 2 4.11 M = 1
30 37 39 46 51 54 58 59 61 63 64 70
1
Introduction and conclusions
Since the successful classification of 6d SCFTs [1–4], there has been considerable interest in classifying 5d SCFTs [5–15] (see also [16]). In this regard, an interesting conjecture was made [8] by observing that there seems to be an upper bound on the number of matter hypermultiplets [7] that can be carried by a supersymmetric 5d gauge theory for it to have a UV completion. At the tip of the bound, the UV completion is a 6d SCFT, and below the bound, the UV completion is a 5d SCFT. Based on this observation, it was conjectured that it should be possible to obtain all 5d SCFTs by systematically integrating out BPS particles from 6d SCFTs compactified on a circle.1 1
Notice that the way this conjecture has been phrased, it not only applies to 5d SCFTs having an effective gauge theory description, but also to 5d SCFTs not having such a gauge theory description. An example of such a 5d SCFT is the theory “su(2) with minus one number of fundamental hypers” which can be obtained by compactifying M-theory on a local P2 .
–1–
JHEP09(2020)007
1 Introduction and conclusions
2
Rank one
Notice that integrating out matter hypermultiplets from a 5d gauge theory does not change the rank of the theory. This generalizes to the fact that integrating out BPS particles from a 5d theory does not change its rank. Thus the KK theories relevant to the classification 2
For generic KK theories, it is a smooth threefold. For some exceptional KK theories, the CalabiYau threefo
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