The aim of this talk is to extract the quadratic corrections to Fronsdal equations from Vasiliev's equations, and discuss their structure. The issue of locality in higher-spin theories will be addressed. Implications of this analysis in relation to Giombi-Yin checks of higher-spin/vector model duality will be discussed. Some of the previous puzzles will be resolved, while others will be elucidated.

We would like to talk about all kinds of supersymmetric and non-supersymmetric scattering amplitudes of type IIA,IIB superstring theory as well as their corrections. In fact we want to address how to get to a universal conjecture for DBI, Chern-Simons and more importantly new Wess Zumino actions with their all order $\alpha'$ corrections. Indeed we try to provide a comprehensive explanation even for D- brane-anti D-brane systems, where various new techniques will be also introduced. If time allows , we then mention several issues related to those effective actions and eventually highlight some comments about higher point functions of the Mixed closed string RR , scalar fields in different pictures of the string theory amplitude.

We study the general formulation of gauged supergravity in seven dimensions with sixteen supercharges keeping duality covariance by means of the embedding tensor formalism. We first classify all inequivalent duality orbits of consistent deformations. Secondly, we analyse the complete set of critical points in a systematic way. Interestingly, we find the first examples of stable de Sitter solutions within a theory with such a large amount of supersymmetry.

We introduce connection, torsion and curvature for Courant algebroids. We discuss in detail torsionless connections compatible with a generalized metric and the related Einstein-Hilbert actions.

We derive the localization formula for N=4 supersymmetric quiver quantum mechanics in the Higgs and Coulomb branch. The partition function (index) is exactly evaluated and it is shown that the path integral is localized at fixed points, which are given by solutions to the BRST equations combined with D-term and F-term conditions. We give various examples of the quiver theory and classifications of their fixed points. The indexes completely agree with the mathematical wall crossing formulae for the quiver moduli spaces. We also discuss a gravitational picture of the localization in the Coulomb branch.

We consider bound states of strings which arise in 6d (1,0) SCFTs that are realized in F-theory in terms of linear chains of spheres with negative self-intersections 1,2, and 4. These include the strings associated to N small E8 instantons, as well as the ones associated to M5 branes probing A and D type singularities in M-theory or D5 branes probing ADE singularities in Type IIB string theory. We find that these bound states of strings admit (0,4) supersymmetric quiver descriptions and show how one can compute their elliptic genera.

Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non AdS space-times, including the near horizon geometry of generic extremal black holes. I’ll explain that WCFTs posses a type of boost symmetry. Using this insight, I’ll discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories will be discussed as well as examples of WCFTs. Lastly I’ll present a systematic description of the holographic duals of WCFTs. I’ll argue that the minimal setup is not Einstein gravity but an SL(2,R) x U(1) Chern-Simons Theory, which we call Lower Spin Gravity.

I will argue that the holographic correspondence can be reconstructed in the large N and strongly interacting limit as a specific generalisation of Wilsonian RG flow, which can be defined via three simple principles. I will also give an explicit example for such a reconstruction, where dual non-linear classical gravity equations in the long wavelength approximation will emerge from specific kinds of coarse graining of hydrodynamics in the field theory.

In this talk I will review some of the main results of my research in this area, which stated in 2007 in collaboration with John L. Cardy and Benjamin Doyon. I will emphasise how a special type of field we have named branch point twist field has become an essential tool for performing computations of the entanglement entropy in non-critical systems. I will show how the relationship between correlators of twist fields and entanglement entropy allows us to recover well-known results for critical systems but also to predict new results for theories with a finite correlation length. Time permitting, I will mention some more recent results extending our understanding to non-unitary critical and non-critical systems.

Half BPS states (operators) in N=4 SYM are famously described by free fermions both at weak and strong coupling. I describe a set of conjectures for a preferred class of states in more general conformal field theories that can be tested in supergravity for when such a free fermion description might arise and some motivation for it applying generally. The states in question belong to the chiral ring of a supersymmetric conformal field theory that extremize an additional U(1) charge for fixed dimension and can be reduced to multi-traces of a composite matrix field, which is equivalent to using Young tableaux (Schur polynomials) as a basis. The main conjecture asserts that if the Young tableaux are orthogonal, then the set of extremal three point functions of traces to order 1/N are determined up to a single constant. The conjecture is extended further by providing an exact norm for the Schur basis and this norm arises from a set of free fermions for a generalized oscillator algebra.

My starting point is a holographic model of the Kondo effect recently proposed by Erdmenger et. al., i.e. of a magnetic impurity interacting with a strongly coupled system. Specifically, I focus on the challenges of computing gravitational backreaction in this model, which demands a study of the Israel junction conditions. I present general results on these junction conditions, including analytical solutions for certain toy models, that may be relevant also more generally in the AdS/boundary CFT correspondence. Furthermore, similar junction conditions for a bulk Chern-Simons field appearing in the holographic Kondo model are discussed. I then focus on the computation and interpretation of entanglement entropy in this holographic model.

I will discuss how to construct rigid supersymmetric gauge theories on Riemannian five-manifolds following a holographic approach. This approach realises the five-manifold as the conformal boundary of a six-dimensional bulk supergravity solution and leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. The background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Finally, I’ll also construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

I will discuss the partition function of 4d N=1 theories on Hopf surfaces. These are diffeomorphic to S^1 x S^3 and the partition function provides a path integral realization of the supersymmetric index. Its large S^1 limit exhibits a universal behaviour associated to the existence of a Casimir energy. I will argue that, contrarily to the non-supersymmetric case, this Casimir energy is a physical (non-ambiguous) quantity in supersymmetric theories.

I will review and discuss in detail type II string theory on $AdS_3\times S^3\times T^4$ and its $1+1$ dimensional superconformal field theory dual, emphasizing the string theoretic aspects of this duality. For one unit of NS-NS 5-brane flux ($Q_5=1$), this string theory has been suggested to be dual to a grand-canonical ensemble of $T^{4N}/S_N$ free symmetric orbifold CFTs, and one goal will be to understand how this is consistent and how it fits with the description of other values of $Q_5$. I will discuss how the strong coupling limit of the NS-NS string theory arises (even at large $N$) in the free orbifold description, and why this limit does not have a weakly coupled R-R description. The dual CFT includes (for all values of $Q_5$) an extra $T^4$ factor that is decoupled from perturbative string theory, and I will discuss how this appears and how it is coupled to the CFT. Based on 2406.14605 with Erez Urbach.

Many gauge theories, such as 3+1d and 2+1d SU(N) gauge theories with N_f massless Dirac fermions in the fundamental representation, exhibit "conformal windows" - a range of values of N_f for which the theory flows to a non-trivial conformal field theory at low energy. It is interesting to ask how these windows end and transition into phases with confinement and with spontaneous breaking of the flavor symmetry. I will begin by reviewing what is known about 3+1 dimensional QCD, focusing on the large N and N_f limit and on the conformal window there, and I will review the standard "merger scenario" for the end of its conformal window. I will then move on to QCD in 2+1 dimensions, and discuss its phase diagram as a function of the mass and of the discrete parameters N, N_f and the Chern-Simons level k, focusing again on the limit of large N, N_f, k. I will argue that this theory also has a conformal window (corresponding to a second order phase transition when changing the mass) but that it does not always end at a merger, and I will suggest two other possibilities for the end of general conformal windows. The different scenarios can be distinguished by the behavior of the theory as the boundary of the conformal window is approached from either side. Based on work in progress with Thomas Dumitrescu, Zohar Komargodski and Jiangyuan Qian.

In this talk I will discuss how to construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2, starting from the four-point correlator of the stress tensor multiplet in N=4 SYM. Unitarity forces the introduction of a scale \Delta_{gap} and these solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. These solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Comparison with such instanton computations allows to fix \Delta_{gap}. Using this gap scale one can explain the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge.

Supergravity theories were once hoped to provide ultraviolet finite theories of quantum gravity without requiring profoundly new physical frameworks. These hopes faded in the 1980s, but renewed efforts in recent years have uncovered some surprising ultraviolet behaviour. In this talk, I will give an overview of the explicit scattering amplitude calculations in perturbative supergravity over the last few years. In particular cases, there are indications of ultraviolet cancellations not accounted for by known symmetry arguments. I will highlight these cases and give some reasons to be optimistic and some reasons to be pessimistic about supergravity as a contender for a quantum theory of gravity.

We review the construction of the so-called λ-deformations of WZW and gauged WZW models. We discuss their integrability and algebraic properties, their behavior under RG flows as well as their embeddings to type-II supergravity.