The Symmetry TFT of a quantum field theory is a Topological Field Theory in one dimension more, that describes the structure of the symmetry, its representations, its anomalies, and the possible topological manipulations (gaugings). Until recently only the case of finite symmetries had been addressed. I will present a proposal for the Symmetry TFT of theories with a U(1) symmetry: it is a BF theory with a continuum of topological operators. I will discuss many examples, including chiral anomalies, 2-groups, the non-invertible Q/Z chiral symmetry in 4d with ABJ anomaly, and I will discuss the non-Abelian case as well.

There exist low-dimensional models of holography in which the bulk gravitational theory is dual to an ensemble average of boundary quantum field theories (as opposed to a single theory). In the case of three-dimensional gravitational theories based on topological field theories, we draw a connection between the ensemble averaging (and the lack of factorization of the partition function) and the presence of global symmetries. Once the global symmetries are removed (by a suitable gauging procedure), the gravitational theory behaves as a unitary quantum system.; Part of London TQFT Journal Club; please register at https://www.london-tqft.co.uk;

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS spacetimes. Black holes correspond to ensembles of states in the boundary field theory. In the presence of supersymmetry, we rephrase the problem of counting those states in terms of a supersymmetric partition function: the superconformal index. By performing a careful analysis of the index of 4d N=4 SU(N) Super-Yang-Mills theory, with the help of a Bethe Ansatz approach, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions, that we are able to identify with complex saddles of the (putative) gravitational path-integral. Along the way we propose a necessary condition for complex saddles to contribute, based on the size of their non-perturbative corrections.

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS space. Black holes should correspond to ensembles of states in the boundary field theory. By analyzing the superconformal index of 4d N=4 SU(N) Super-Yang-Mills, with the help of a new Bethe Ansatz type formula, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions and Stokes phenomena, hinting at new physics.

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS space. Black holes should correspond to ensembles of states in the boundary field theory. By analyzing the superconformal index of 4d N=4 SU(N) Super-Yang-Mills, with the help of a new Bethe Ansatz type formula, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions and Stokes phenomena, hinting at new physics.

One of the great successes of string theory, as a theory of quantum gravity, is the explanation of the entropy of asymptotically-flat black holes. I will present, instead, a counting of the microstates of certain black holes in AdS4. The black holes have an holographic description as RG flows from a 3D CFT to superconformal quantum mechanics, and the counting of microstates proceeds via supersymmetric localization. Along the way, we will define and compute an index for topologically twisted theories, and propose an extremization principle to determine the superconformal R-symmetry in quantum mechanics.

I present new analytic solutions of type IIB supergravity with fully backreacting D7-branes describing the addition of an arbitrary number of flavors to the Klebanov-Tseytlin and Klebanov-Strassler theories. I provide a detailed analysis of the field theory and of the duality cascade which describes its RG flow, Seiberg duality is understood as a large gauge transformation in supergravity. Moreover the string background suggests that the UV behavior is a duality wall.