It was previously noted that for 3d SCFTs with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  ≥ 6 the moduli space has the form of ℂ4r  /Γ, where Γ is a complex reflection group, at least following suitable gauging of finite symmetries. Here we argue that this observation can be extended also to 3d SCFTs with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  ≥ 5 SUSY, where Γ is now a quaternionic reflection group. To do this, we study the moduli space of the known 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 5 SCFTs. For Lagrangian cases, the results for the moduli space are further checked using the superconformal index.

United States

Anirudh Deb

Israel

Gabi Zafrir

<math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 5 SCFTs and quaternionic reflection groups

Recently there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertible symmetries, in four dimensions. In this paper we shall examine what happens to this structure when the 4d theory is compactified to lower dimensions, specifically to 3d and 2d, where we shall be mainly interested in generalized symmetry structures whose origin can be linked to mixed flavor-gauge anomalies. We discuss several aspects of the compactification, and in particular argue that under certain conditions the discussed generalized symmetry structure may trivialize in the infrared. Nevertheless, we show that even when this happens the presence of the 4d generalized symmetry structure may still leave an imprint on the low-energy theory in terms of additional ’t Hooft anomalies or by breaking part of the symmetry. We apply and illustrate this using known examples of compactifications from four dimensions, particularly, the reduction of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 U(N  c ) SQCD on a circle to 3d and on a sphere to 2d.

Japan

Emily Nardoni

United Kingdom

Matteo Sacchi

Orr Sela

Yunqin Zheng

Dimensionally reducing generalized symmetries from (3+1)-dimensions

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O7+-plane and O7 − -plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O7+-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points.

South Korea

Hee-Cheol Kim

Minsung Kim

China

Sung-Soo Kim

Superconformal indices for non-Lagrangian theories in five dimensions

Much insight into the dynamics of quantum field theories can be gained by studying the relationship between field theories in different dimensions. An interesting observation is that when two theories are related by dimensional reduction on a compact surface, their ’t Hooft anomalies corresponding to continuous symmetries are also related: the anomaly polynomial of the lower-dimensional theory can be obtained by integrating that of the higher-dimensional one on the compact surface. Naturally, this relation only holds if both theories are even dimensional. This raises the question of whether similar relations can also hold for the case of anomalies in discrete symmetries, which might be true even in odd dimensions. The natural generalization to discrete symmetries is that the anomaly theories, associated with the lower and higher dimensional theories, would be related by reduction on the compact surface. We explore this idea for compactifications of 5d superconformal field theories (SCFTs) to 3d on Riemann surfaces with global-symmetry fluxes. In this context, it can be used both as a check for these compactification constructions and for discovering new anomalies in the 5d SCFTs. This opens the way to applying the same idea of dimensional reduction of the anomaly theory to more general types of compactifications.

5d to 3d compactifications and discrete anomalies

It is known that the ’t Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood for non-invertible symmetries. In this note we discuss how the linking invariants in a non-invertible TQFT known as the Symmetry TFT (SymTFT) can be used as a diagnostic for ’t Hooft anomalies of non-invertible symmetries. When the non-invertible symmetry is non-intrinsically non-invertible, and hence the SymTFT is a Dijkgraaf-Witten model, the linking invariants can be computed explicitly. We illustrate this proposal through the examples of the abelian Higgs model in 2d, as well as adjoint QCD and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills in 4d. We also comment on how the ’t Hooft anomalies of non-invertible symmetries impose new constraints on the dynamics.

Justin Kaidi

Symmetry TFTs and anomalies of non-invertible symmetries

Many interesting phenomena in quantum field theory such as dualities and symmetry enhancements can be understood using higher dimensional constructions. In this paper, we study compactifications of the rank 1 5d Seiberg   <math> <msub> <mi>E</mi> <msub> <mi>N</mi> <mrow> <mi>f</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> </math>  $$ {E}_{N_{f+1}} $$  SCFTs to 3d on Riemann surfaces of genus g &gt; 1. We rely on the recent progress in the study of compactifications of 6d SCFTs to 4d and torus compactifications of 5d SCFTs to conjecture 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 theories corresponding to the reduction of said 5d SCFTs on three punctured spheres. These can then be used to build 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 models corresponding to compactifications on more general surfaces. The conjectured theories are tested by comparing their properties against those expected from the compactification picture.

Trinions for the 3d compactification of the 5d rank 1   <math> <msub> <mi>E</mi> <msub> <mi>N</mi> <mrow> <mi>f</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> </math>  $$ {E}_{N_{f+1}} $$  SCFTs

It is expected on general grounds that the moduli space of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theories is of the form ℂ3r  /Γ, with r the rank and Γ a crystallographic complex reflection group (CCRG). As in the case of Lie algebras, the space of CCRGs consists of several infinite families, together with some exceptionals. To date, no 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theory with moduli space labelled by an exceptional CCRG (excluding Weyl groups) has been identified. In this work we show that the 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theories proposed in [1], constructed via non-geometric quotients of type-  <math> <mi>e</mi> </math>  $$ \mathfrak{e} $$  6d (2,0) theories, realize nearly all such exceptional moduli spaces. In addition, we introduce an extension of this construction to allow for twists and quotients by outer automorphism symmetries. This gives new examples of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theories going beyond simple S-folds.

Mario Martone

Exceptional moduli spaces for exceptional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theories

Non-invertible symmetries have recently been understood to provide interesting constraints on RG flows of QFTs. In this work, we show how non-invertible symmetries can also be used to generate entirely new RG flows, by means of so-called non-invertible twisted compactification. We illustrate the idea in the example of twisted compactifications of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills (SYM) to three dimensions. After giving a catalogue of non-invertible symmetries descending from Montonen-Olive duality transformations of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM, we show that twisted compactification by non-invertible symmetries can be used to obtain 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 6 theories which appear otherwise unreachable if one restricts to twists by invertible symmetries.

Non-invertible symmetries of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM and twisted compactification

We study the 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 theories resulting from the compactification of a family of 5d SCFTs on a torus with flux in the global symmetry. The family of 5d SCFTs used in the analysis is the one that UV completes the 5d SU(N + 1) gauge theories with Chern-Simons level k and N  f  fundamental hypermultiplets, generalizing the previous investigation of the torus compactifications of the rank 1 Seiberg   <math> <msub> <mi>E</mi> <msub> <mi>N</mi> <mrow> <mi>f</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> </math>  $$ {E}_{N_{f+1}} $$  SCFT (which is the N = 1 member of the family). This construction systematically yields three-dimensional theories presenting highly non-trivial non-perturbative phenomena such as infra-red dualities and enhanced symmetries, which we check using various methods.

Italy

On the 3d compactifications of 5d SCFTs associated with SU(N + 1) gauge theories

In this note we construct magnetic quivers for the known rank-2 four dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories. For every rank-1 theory one can find a unitary magnetic quiver; we observe that this is no longer possible at rank 2. Our list of magnetic quivers necessarily includes orthosymplectic quivers, in addition to unitary ones, of both the simply and non simply laced variety. Using quiver subtraction, one can compute Higgs branch Hasse diagrams and compare with the results obtained via other methods finding nearly perfect agreement.