Two-dimensional Conformal Field Theories (CFTs) are defined via a list of primary operators, along with their scaling dimensions, spins and OPE coefficients. This set of data, along with the central charge, uniquely defines any correlation function of the theory on an arbitrary Riemann surface. Using consistency conditions like crossing symmetry and modular invariance, one can show that there...

Reversing the logic of the bootstrap approach in Liouville CFT we explicitly compute the connection formulae for degenerate conformal blocks. In the semiclassical limit of the theory, this amounts to solving the connection problem of Fuchsian ODEs. Generalizing to irregular insertions we solve as well for various confluences. Concentrating on the Heun equation and its confluences, we can solve...

We show how to construct an explicit map between boundary states and quantum gravity states in AdS/CFT via a specific field theory path integral on a bulk Cauchy slice, rather than on the asymptotic boundary. The field theory is constructed from the boundary CFT via an irrelevant deformation, which is the analogue of the well-known $T\bar{T}$ operator in two boundary dimensions. Our...

Fractons are quasiparticles with the distinctive feature of having only limited mobility. This bizarre trait and their unusual symmetries also make the coupling to curved spacetime nontrivial. I will show how aristotelian geometry provides the right framework, review the state-of-the-art on this issue, provide a novel no-go theorem for theories with linear dipole symmetry, spatial derivatives...

4d holomorphic QFTs (such as those obtained from twisting N=1 QFTs) are endowed with extra structures and symmetries which are a 4d analogue of a 2d chiral algebra. In this talk, I will describe these holomorphic theories, higher structures that arise in studying loop corrections to the BRST differential, and a recursive "bootstrap" procedure for systematically computing these loop...

The conformal data of generic CFTs involving heavy charged operators can be organised as a series in inverse powers of the global charges involved. When extrapolating these expansions to light low-charge sectors, is it relevant to ask whether these series are divergent and Borel-summable. In this talk, I will show that the O(N) scalar CFT has a large-charge expansion which is not...

In the matrix quantum mechanics (MQM) dual to the non-supersymmetric 2d black hole, we identify a set of degenerate states as the black hole microstates. At leading order in large $N$, the log of number of these states (already calculated by Gross and Klebanov) matches the Bekenstein-Hawking entropy formula, and also agrees with one of two candidates found by Kazakov and Tseytlin. The mass...

I will discuss the analytic bootstrap technique applied to holographic superconformal field theories. In particular I will focus on $\mathcal{N}=4$ Super Yang-Mills and study correlators of quarter-BPS operators. Despite the fact that they are less protected than their half-BPS counterparts, these correlators can be constrained via the chiral algebra twist and this information is enough to...