We study the anomalies of two-dimensional BPS defects in six-dimensional $$ \mathcal{N} $$ = (1 0) superconformal field theories. Using a holographic description of these defects furnished by probe D4-branes in AdS solutions of ten-dimensional type IIA supergravity, we compute the two independent defect Weyl anomalies from the on-shell action for a spherical defect and defect sphere entanglement entropy. We find agreement between the holographic prediction for the defect A-type anomaly coming from the defect sphere free energy and the leading large contribution to the defect ’t Hooft anomaly found using anomaly inflow. We also find agreement between the holographic computation of the expectation value of a surface operator wrapping a torus and the supersymmetric localization computation for a circular Wilson loop in $$ \mathcal{N} $$ = 1 super Yang-Mills theory on . Lastly, we holographically compute the defect gravitational anomaly from the Wess-Zumino action of the probe D4-brane, which provides a subleading large correction to the defect A-type anomaly.

Italy

Fabio Apruzzi

Thailand

Noppadol Mekareeya

Brandon Robinson

Alessandro Tomasiello

Superconformal anomalies for string defects in six-dimensional

ℤ n  S-folds of 5d SCFTs, including T  N , which lead to brane webs with E 6,7,8 7-branes were discussed recently in [1, 2]. We generalize the construction to ‘fractional quotients’, which are based on ℤ n  actions linking multiple copies of the seed theory and lead to H 0,1,2 7-branes. We provide the holographic duals for both classes. This expands the space of explicitly known Type IIB AdS6 solutions by incorporating F-theory 7-branes of type E 6,7,8 and H 0,1,2, extending previous constructions for O7-planes. We discuss observables including the free energies and link the results to matrix model descriptions.

Switzerland

Israel

Oren Bergman

South Korea

Hee-Cheol Kim

United Kingdom

United States

Christoph Uhlemann

Generalized quotients and holographic duals for 5d S-fold SCFTs

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.

Ibrahima Bah

Federico Bonetti

Sakura Schäfer-Nameki

Noninvertible Symmetries from Holography and Branes

Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.

Higher form symmetries TFT in 6d

We discuss infinite families of non-supersymmetric AdS6 solutions in Type IIB string theory. They are siblings of supersymmetric solutions which are associated with (p, q) 5-brane webs and holographically dual to 5d SCFTs engineered by those brane webs. The non-supersymmetric backgrounds carry identical 5-brane charges and are connected to the supersymmetric ones by RG flows. We study the stability of the non-supersymmetric solutions, identifying perturbative and non-perturbative decay channels for all the backgrounds explicitly available. We also identify likely decay mechanisms for solutions that have not been constructed explicitly but may be expected to exist based on brane web considerations. Finally, we exclude scale separation by constructing universal spin 2 modes with masses comparable to the mass-scale of the cosmological constant.

G. Luca

Sweden

France

Gabriele Monaco

Non-supersymmetric AdS 6 and the swampland

We study confinement in 4d <math><mi>N</mi><mo>=</mo><mn>1</mn></math> <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Super-Yang Mills (SYM) from a holographic point of view, focusing on the 1-form symmetry and its relation to chiral symmetry breaking (<math><msub><mi>χ</mi><mi>SB</mi></msub></math>). We identify the topological couplings in the 5d truncation of the Klebanov-Strassler solution that determine the 1-form symmetry and its ’t Hooft anomalies. One coupling is a mixed 0-/1-form symmetry anomaly related to <math><msub><mi>χ</mi><mi>SB</mi></msub></math> in gapped confining vacua. In the gravity dual we also identify the infrared 4d topological field theory which realizes <math><msub><mi>χ</mi><mi>SB</mi></msub></math> and matches the mixed anomaly. Finally, complementing this, we derive the chiral and mixed anomalies from the little string theory realization of pure SYM.

Marieke van Beest

Dewi S. W. Gould

Holography, 1-form symmetries, and confinement

We systematically analyse 5d superconformal field theories (SCFTs) obtained by dimensional reduction from 6d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (1, 0) SCFTs. Such theories have a realization as M-theory on a singular Calabi-Yau threefold, from which we determine the so-called combined fiber diagrams (CFD) introduced in [1–3]. The CFDs are graphs that encode the superconformal flavor symmetry, BPS states, low energy descriptions, as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from 6d, there are two approaches: the first is to consider a circle-reduction combined with mass deformations. The second is to circle-reduce and decouple an entire gauge sector from the theory. The former is applicable e.g. for very Higgsable theories, whereas the latter is required to obtain a 5d SCFT from a non-very Higgsable 6d theory. In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descend from non-Higgsable clusters and non-minimal conformal matter theories. Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs.

Yi-Nan Wang

5d SCFTs from decoupling and gluing

AdS7 supersymmetric solutions in type IIA have been classified, and they are infinitely many. Moreover, every such solution has a non-supersymmetric sister. In this pa- per, we study the perturbative and non-perturbative stability of these non-supersymmetric solutions, focusing on cases without orientifolds. Perturbatively, we first look at the KK spectrum of spin-2 excitations. This does not exhibit instabilities, but it does show that there is no separation of scales for either the BPS and the non-BPS case, thus proving for supersymmetric AdS7 a well-known recent conjecture. We then use 7d gauged supergravity and a brane polarization computation to access part of the spectrum of KK scalars. The result signals an instability for all non-supersymmetric solutions except those that have a single D8 on each side. We finally look at non-perturbative instabilities, and find that NS5 bubbles make these remaining solutions decay.

CERN

Alessandra Gnecchi

On AdS7 stability

We propose a generalization of <math><mi>S</mi></math>-folds to 4d <math><mi>N</mi><mo>=</mo><mn>2</mn></math> theories. This construction is motivated by the classification of rank one 4d <math><mi>N</mi><mo>=</mo><mn>2</mn></math> super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a configuration of <math><mi>N</mi><mo>=</mo><mn>2</mn></math> <math><mi>S</mi></math>-folds combined with 7-branes. The main advantage of this point of view is that realizes both Coulomb and Higgs branch flows and allows for a straightforward generalization to higher rank theories.

Simone Giacomelli

4d <math><mi>N</mi><mo>=</mo><mn>2</mn></math> <math><mi>S</mi></math>-folds

We present a general prescription for determining the global <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> symmetries of six-dimensional superconformal field theories. We use the quiverlike gauge theory description of the tensor branch to identify candidate <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> symmetries which can act on generalized matter. The condition that these candidate <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>’s are free of Adler-Bell-Jackiw anomalies provides bottom-up constraints for <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>’s. This agrees with the answer obtained from symmetry breaking patterns induced by Higgs branch flows. We provide numerous examples illustrating the details of this proposal. In the F-theory realization of these theories, some of these symmetries originate from deformations of non-Abelian flavor symmetries localized on a component of the discriminant, while others come from an additional generator of the Mordell-Weil group. We also provide evidence that some of these global <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>’s do not arise from gauge symmetries, as would happen in taking a decoupling limit of a model coupled to six-dimensional supergravity.

Marco Fazzi

Jonathan J. Heckman

Tom Rudelius

Hao Y. Zhang

General prescription for global <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>’s in 6D SCFTs