We revisit 6d (2,0) SCFTs of type and their realization in M-theory, focusing on absolute variants of these theories and on their global finite 0- and 2-form symmetries. We derive the 7d SymTFT capturing these global symmetries from M-theory, both from the point of view of the low-energy supergravity action on × and from M2- and M5-branes giving rise to its topological operators. Along the way, results by Gukov, Hsin, and Pei are extended by keeping track of an additional 7d gauge field, associated to the outer automorphism of the algebra. In particular, we find an interplay of non-invertible symmetries and mixed anomalies for absolute 6d (2,0) SCFTs with ≥ 1. We highlight several subtle points related to the non-orientability of , the half-integral -flux that threads it, and the non-commutativity of fluxes. All these also play an essential role in a holographic derivation of the anomaly polynomial of 6d (2,0) SCFTs.

Spain

Federico Bonetti

Sweden

Michele Zotto

France

Ruben Minasian

SymTFTs and non-invertible symmetries of 6d (2,0) SCFTs of type

In this paper, we present a unified perspective on sphere consistent truncations based on the classical geometric properties of sphere bundles. The backbone of our approach is the global angular form for the sphere. A universal formula for the Kaluza-Klein ansatz of the flux threading the n-sphere captures the full nonabelian isometry group SO(n + 1) and scalar deformations associated to the coset SL(n + 1, ℝ)/SO(n + 1). In all cases, the scalars enter the ansatz in a shift by an exact form. We find that the latter can be completely fixed by imposing mild conditions, motivated by supersymmetry, on the scalar potential arising from dimensional reduction of the higher dimensional theory. We comment on the role of the global angular form in the derivation of the topological couplings of the lower-dimensional theory, and on how this perspective could provide inroads into the study of consistent truncations with less supersymmetry.

United Kingdom

Germany

Valentí Camell

United States

Peter Weck

Consistent truncations from the geometry of sphere bundles

We propose a systematic approach to deriving symmetry generators of quantum field theories in holography. Central to this analysis are the Gauss law constraints in the Hamiltonian quantization of symmetry topological field theories (SymTFTs), which are obtained from supergravity. In turn, we realize the symmetry generators from world-volume theories of D-branes in holography. Our main focus is on noninvertible symmetries, which have emerged in the past year as a new type of symmetry in <math><mi>d</mi><mo>≥</mo><mn>4</mn></math> QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> Super-Yang Mills. In the brane picture, the fusion of noninvertible symmetries naturally arises from the Myers effect on D-branes. In turn, their action on line defects is modeled by the Hanany-Witten effect.

Switzerland

Fabio Apruzzi

Ibrahima Bah

Sakura Schäfer-Nameki

Noninvertible Symmetries from Holography and Branes

We present new families of AdS 5 solutions in M-theory preserving 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supersymmetry. We perform a systematic analysis of holographic observables for these solutions, providing evidence for an interpretation in terms of 4d superconformal field theories (SCFTs) of Argyres-Douglas type, realized in class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  via a sphere with one irregular, and one regular puncture. The gravity solutions exhibit internal M5-brane sources that correspond to the irregular puncture. For a family of solutions, we identify explicitly the class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  puncture data and perform a detailed match, including Higgs branch operators. For other families we comment on proposed field theory duals, based on irregular punctures labeled by nested Young tableaux.

Japan

Emily Nardoni

Thomas Waddleton

Aspects of irregular punctures via holography

We analyze the global symmetries and anomalies of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 field theories that arise from a stack of N M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved ℂ2 /ℤ k  singularity fibered over a smooth Riemann surface of genus g ≥ 2, supported by a non-trivial G 4-flux configuration labeled by a collection of 2(k − 1) flux quanta, {N  i }. For k = 2, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit AdS5 solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to k ≥ 3 is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the ’t Hooft anomalies for continuous symmetries at leading order in the limit of large N, N  i .

Enoch Leung

M5-branes probing flux backgrounds

We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of N M5-branes probing a ℂ2 /ℤ k  singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved ℂ2 /ℤ k  singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of a class of modes that decouple along the RG flow from six to four dimensions, for generic N, k, and genus. These modes are identified with the flip fields encountered in the Lagrangian descriptions of these 4d models, when they are available. We show that such fields couple to operators originating from M2-branes wrapping the resolution cycles. This provides a geometric origin of flip fields. They interpolate between the 6d theory in the UV, where the M2-brane operators are projected out, and the 4d theory in the IR, where these M2-brane operators are part of the spectrum.

The geometry of decoupling fields

We initiate a study of the holographic duals of a class of four-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS 5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large-N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality.

M5-brane sources, holography, and Argyres-Douglas theories

We propose the first explicit holographic duals for a class of superconformal field theories of Argyres-Douglas type, which are inherently strongly coupled and provide a window onto remarkable nonperturbative phenomena (such as mutually nonlocal massless dyons and relevant operators of fractional dimension). The theories under examination are realized by a stack of <math><mi>M</mi><mn>5</mn></math>-branes wrapped on a sphere with one irregular puncture and one regular puncture. In the dual <math><mn>11</mn><mi>d</mi></math> supergravity solutions, the irregular puncture is realized as an internal <math><mi>M</mi><mn>5</mn></math>-brane source.

Holographic Duals of Argyres-Douglas Theories

We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to AdS 5. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their ’t Hooft anomalies for 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a ℤ2 orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.

Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

We extend the anomaly inflow methods developed in M-theory to SCFTs engineered via D3-branes in type IIB. We show that the ’t Hooft anomalies of such SCFTs can be computed systematically from their geometric definition. Our procedure is tested in several 4d examples and applied to 2d theories obtained by wrapping D3-branes on a Riemann surface. In particular, we show how to analyze half-BPS regular punctures for 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM on a Riemann surface. We discuss generalizations of this formalism to type IIB configurations with F 3, H 3 fluxes, as well as to F-theory setups.