Symmetry TFTs from String Theory.

We determine the d+1 dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for d-dimensional QFTs obtained by compactifying M-theory on a non-compact space X. The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary ∂X of the space X. Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space ∂X, which in turn gives rise to the background fields for discrete (in particular higher-form) symmetries. We apply this framework to 7d super-Yang Mills, where X=C2/ΓADE, as well as the Sasaki-Einstein links of Calabi-Yau three-fold cones that give rise to 5d superconformal field theories. This M-theory analysis is complemented with a IIB 5-brane web approach, where we derive the SymTFTs from the asymptotics of the 5-brane webs. Our methods apply to both Lagrangian and non-Lagrangian theories, and allow for many generalisations.

Noninvertible Symmetries from Holography and Branes.

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 d≥4 QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4D N=1 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.

Six-Dimensional Superconformal Theories and their Compactifications from Type IIA Supergravity.

We describe three analytic classes of infinitely many AdS(d) supersymmetric solutions of massive IIA supergravity, for d=7,5,4. The three classes are related by simple universal maps. For example, the AdS(7)×M(3) solutions (where M(3) is topologically S(3)) are mapped to AdS(5)×Σ(2)×M(3)', where Σ(2) is a Riemann surface of genus g≥2 and the metric on M(3)' is obtained by distorting M(3) in a certain way. The solutions can have localized D6 or O6 sources, as well as an arbitrary number of D8-branes. The AdS(7) case (previously known only numerically) is conjecturally dual to an NS5-D6-D8 system. The field theories in three and four dimensions are not known, but their number of degrees of freedom can be computed in the supergravity approximation. The AdS(4) solutions have numerical "attractor" generalizations that might be useful for flux compactification purposes.

Erratum to: AdS6 solutions of type II supergravity.

[This corrects the article DOI: 10.1007/JHEP11(2014)099.].