4d N $$ \mathcal{N} $$ =2 theories with disconnected gauge groups

We initiate the bootstrap program for N = 3 superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a 2d chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of N = 3 theories. With the goal of describing a protected subsector of a family of N = 3 SCFTs, we propose a new 2d chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory. Turning to the crossing equations, we work out the superconformal block expansion and apply standard numerical bootstrap techniques in order to constrain the CFT data. We obtain bounds valid for any theory but also, thanks to input from the chiral algebra results, we are able to exclude solutions with N = 4 supersymmetry, allowing us to zoom in on a specific N = 3 SCFT.

Section: Jhep04(2017)032mentioning

confidence: 94%

“…N = 3 SCFTs, but also led to new ones [8,10]. Some of these theories are obtained by starting from N = 4 SYM with gauge group U(1) or SU (2) and gauging discrete symmetries, while others correspond to genuine N = 3 SCFTs which are not obtained by discrete gauging.…”

Section: Jhep04(2017)032mentioning

confidence: 99%

Bootstrapping N = 3 $$ \mathcal{N}=3 $$ superconformal theories

Lemos

Liendo

Meneghelli

et al. 2017

“…The Néron-Severi group NS(E) ∼ = Pic(E)/Pic(E) 0 is then a unimodular (odd) lattice of signature (1,9). In facts E, being a relatively minimal rational elliptic surface with section, is just P 2 blown-up at 9 points (see Theorem 5.6.1 of [27] or section VIII.1 of [25]).…”

Section: Jhep08(2018)057mentioning

confidence: 99%

“…In this case p g (E) = 0, ̺(E) = 10, and NS(E) is an (odd) unimodular lattice of signature (1,9); by general theory it is isomorphic to…”

Section: Review: Néron-severi and Mordell-weil Groupsmentioning

confidence: 99%

“…At the coarse-grained level one lists the allowed k-tuples {∆ 1 , ∆ 2 , · · · , ∆ k } of dimensions of operators generating the Coulomb branch (see refs. [7][8][9] for recent progress on this problem). Then we have the fine classification of the physically inequivalent models belonging to each coarse-grained class, that is, the list of the distinct QFT which share the same dimension k-tuple.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Special arithmetic of flavor

Caorsi

Cecotti

2018

Abstract:We revisit the classification of rank-1 4d N = 2 QFTs in the spirit of Diophantine Geometry, viewing their special geometries as elliptic curves over the chiral ring (a Dedekind domain). The Kodaira-Néron model maps the space of non-trivial rank-1 special geometries to the well-known moduli of pairs (E, F ∞ ) where E is a relatively minimal, rational elliptic surface with section, and F ∞ a fiber with additive reduction. Requiring enough Seiberg-Witten differentials yields a condition on (E, F ∞ ) equivalent to the "safely irrelevant conjecture". The Mordell-Weil group of E (with the Néron-Tate pairing) contains a canonical root system arising from (−1)-curves in special position in the Néron-Severi group. This canonical system is identified with the roots of the flavor group F: the allowed flavor groups are then read from the Oguiso-Shioda table of Mordell-Weil groups. Discrete gaugings correspond to base changes. Our results are consistent with previous work by Argyres et al.

More on $$ \mathcal{N} $$ =2 S-folds

Giacomelli

Martone

Tachikawa

et al. 2021

Self Cite

We carry out a systematic study of 4d $$ \mathcal{N} $$ N = 2 preserving S-folds of F-theory 7-branes and the worldvolume theories on D3-branes probing them. They consist of two infinite series of theories, which we denote following [1, 2] by $$ {\mathcal{S}}_{G,\mathrm{\ell}}^{(r)} $$ S G , ℓ r for ℓ = 2, 3, 4 and $$ {\mathcal{T}}_{G,\mathrm{\ell}}^{(r)} $$ T G , ℓ r for ℓ = 2, 3, 4, 5, 6. Their distinction lies in the discrete torsion carried by the S-fold and in the difference in the asymptotic holonomy of the gauge bundle on the 7-brane. We study various properties of these theories, using diverse field theoretical and string theoretical methods.