We study the Coulomb branch of class S k $$ {\mathcal{S}}_k $$ N $$ \mathcal{N} $$ = 1 SCFTs by constructing and analyzing their spectral curves.

Romania

Germany

Ioana Coman

Greece

Elli Pomoni

Japan

Masato Taki

South Korea

Futoshi Yagi

Spectral curves of N $$ \mathcal{N} $$ = 1 theories of class S k $$ {\mathcal{S}}_k $$

We propose new five-dimensional gauge theory descriptions of six-dimensional N $$ \mathcal{N} $$ = (1 , 0) superconformal field theories arising from type IIA brane configurations includ-ing an ON 0 -plane. The new five-dimensional gauge theories may have SO, Sp , and SU gauge groups and further broaden the landscape of ultraviolet complete five-dimensional N $$ \mathcal{N} $$ = 1 supersymmetric gauge theories. When we include an O 8 − -plane in addition to an ON 0 -plane, T-duality yields two O 7 − -planes at the intersections of an ON 0 -plane and two O 5 0 -planes. We propose a novel resolution of the O 7 − -plane with four D7-branes in such a configuration, which enables us to obtain three different types of five-dimensional gauge theories, depending on whether we resolve either none or one or two O 7 − -planes. Such different possibilities yield a new five-dimensional duality between a D-type SU quiver and an SO − Sp quiver theories. We also claim that a twisted circle compactification of a six-dimensional superconformal field theory may lead to a five-dimensional gauge theory different from those obtained through a simple circle compactification.

Spain

Hirotaka Hayashi

China

Sung-Soo Kim

Kimyeong Lee

More on 5d descriptions of 6d SCFTs

Yuto Ito

Takuya Okuda

Erratum to: Line operators on S 1 × ℝ 3 $$ {S}^1\times {\mathrm{\mathbb{R}}}^3 $$ and quantization of the Hitchin moduli space

We propose a new 5d description of the circle-compactified 6d (D  N + 4 , D  N + 4) minimal conformal matter theory which can be approached by the 6d  <math><mi>N</mi><mo>=</mo><mfenced><mn>1</mn><mn>0</mn></mfenced></math> $$ \mathcal{N}=\left(1,0\right) $$ Sp(N) gauge theory with N  f  = 2N + 8 flavors and one tensor multiplet. Compactifying the brane set-up for the 6d theory, we arrive at a 5-brane Tao diagram for 5d  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ SU(N + 2) theory of the vanishing Chern-Simons level with 2N + 8 flavors. We conjecture that the 6d theory is recovered as the UV fixed point of this 5d theory. We show that the global symmetry of this 5d theory is SO(4N + 16) identical to that of the 6d theory by analyzing the 7-brane monodromy. By using the Tao diagram, we also find the instanton fugacity is exactly given by the circle radius. By decoupling flavors in this 5d theory, one can obtain all the 5d SU(N + 2) gauge theories of various Chern-Simons levels and corresponding enhanced global symmetries at the 5d UV fixed point.

A new 5d description of 6d D-type minimal conformal matter

We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local K3 surface.

Tao probing the end of the world

We show that the 5D Nekrasov partition functions enjoy the enhanced global symmetry of the UV fixed point. The fiber-base duality is responsible for the global symmetry enhancement. For SU(2) with N f ≤ 7 flavors the fiber-base symmetry together with the manifest flavor SO(2 N f ) symmetry generate the E N f + 1 $$ {\mathrm{E}}_{N_{f+1}} $$ global symmetry, while in the higher rank case the manifest global symmetry of the two dual theories related by the fiber-base duality map generate the symmetry enhancement. The symmetry enhancement at the level of the partition function is manifest once we chose an appropriate reparametrization for the Coulomb moduli.

Vladimir Mitev

Fiber-base duality and global symmetry enhancement

In this article we use 5-brane junctions to study the 5D T N SCFTs corresponding to the 5D $ \mathcal{N} $  = 1 uplift of the 4D $ \mathcal{N} $  = 2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D super-conformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n -point functions of the q -deformed W N Toda theories.

Sweden

Ling Bao

Italy

Non-Lagrangian theories from brane junctions