We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that parity invariant interactions respecting general covariance lead to a reconstruction of Conformal Gravity in even dimensions. In this case the unitarity is sacrificed. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but the parity-odd cubic vertex cannot be written in usual metric variables. We comment on possible approaches that may allow for the formulation of this theory. Finally, by relaxing the general covariance, we show that a non-minimal coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory, that necessarily involves mixed-symmetry fields.

In this seminar I will discuss a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. We show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement.

I review how integrability allows us to explore the planar limit of the AdS/CFT correspondence for arbitrary values of the t'Hooft coupling. In string theory integrability of the 2D σ-model is closely related to Poisson-Lie Symmetry. Double Field Theory can be used to make this symmetry manifest and therewith provides a new tool to study the implications for the gravity side of the correspondence.

We investigate holographic complexity for eternal black hole backgrounds perturbed by shock waves, with both the complexity=action (CA) and complexity=volume (CV) proposals. We consider Vaidya geometries describing a thin shell of null fluid with arbitrary energy falling in from one of the boundaries of a two-sided AdS-Schwarzschild spacetime. We demonstrate how scrambling and chaos are imprinted in the complexity of formation and in the full time evolution of complexity via the switchback effect for light shocks, as well as analogous properties for heavy ones.

I will discuss novel effective field theories for hydrodynamics. After identifying the relevant low-energy degrees of freedom, I will show how the symmetries of the problem can be efficiently implemented using supersymmetry. Interestingly, a conserved entropy current naturally arises as a Noether current in superspace. If time permits, I will also show how to derive such effective actions from holography.

Gravity theories naturally allow for edge states generated by non-trivial boundary-condition preserving diffeomorphisms. I present a specific set of boundary conditions inspired by near horizon physics, show that it leads to soft hair excitations of black hole solutions and discuss implications for black hole entropy.

2D rational conformal field theories (RCFTs) are typically thought of as being the “nicest” interesting CFTs we can study: They have large enough symmetry so that there are only a finite number of primary fields, but they also have applications to the real world (e.g., to various condensed matter systems). In this talk, I will describe a program that aims to understand connections between exotic 4D theories with N=2 superconformal symmetry and more down-to-earth 2D RCFTs, thereby enriching our understanding of both.

There are many reasons to consider perturbative QFT around curved backgrounds, but it is often difficult to perform explicit computations in these settings. Progress in the study of scattering amplitudes (around a trivial background) suggests alternative perspectives to space-time Lagrangians and Feynman rules which could enable progress in the study of scattering on curved backgrounds. I will discuss one such alternative, known as double copy, with a particular focus on gluon and graviton scattering around non-linear plane wave backgrounds

I will revisit the well-known construction of 5d SCFTs from M-theory on a CY3 singularity. Upon massive deformation, such 5d SCFTs are often expected to have 5d N=1 supersymmetric gauge theory descriptions at low energy. I will present a new way to study these 5d ``gauge theory phases'' systematically using type-IIA string theory, and I will comment on the phenomenon of "UV duality." Along the way, I will discuss some slightly subtle properties of the 5d N=1 Coulomb branch prepotential.

In two dimensional topological phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a uniquely practical route to building a quantum computer. Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to strontium ruthenate to semiconductor-superconductor junctions to quantum wires to spin systems to graphene to cold atoms.

The geometry of the moduli space of 4d \mathcal{N}=2 moduli spaces, and in particular of their Coulomb branches (CBs), is very constrained. In this talk I will show that through its careful study, we can learn general and somewhat surprising lessons about the properties of \mathcal{N}=2 super conformal field theories (SCFTs). Specifically I will show that we can prove that the scaling dimension of CB coordinates, and thus of the corresponding operator at the SCFT fixed point, has to be rational and it has a rank-dependent maximum value and that in general the moduli spaces of \mathcal{N}=2 SCFTs can have metric singularities as well as complex structure singularities. Finally I will outline how we can explicitly perform a classification of geometries of \mathcal{N}\geq3 SCFTs and carry out the program up to rank-2. The results are surprising and exciting in many ways.

The AdS/CFT duality maps supersymmetric heavy operators with conformal dimension of the order of the central charge to asymptotically AdS supergravity solutions. I'll show how, by studying the quadratic fluctuations around such backgrounds, it is possible to derive 4-point correlators of two light and two heavy states in the supergravity approximation. Then by using this input, I'll discuss how to reconstruct standard supergravity correlators between four (single particle) operators. I'll present some explicit examples in the AdS3 setup relevant for the duality with the D1-D5 CFT.

I will adapt the Goldstone theorem to spontaneously broken boosts, and show that, while still predicting gapless Goldstone states, it is quite forgiving regarding the nature of such states. In particular, I will show that while for solids and superfluids the role of the boost Goldstone states is played by phonon single-particle states, for a Fermi liquid such a role is played by the particle-hole continuum, that is, by two-particle states.