In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. We provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III_1 von Neumann algebraic structure from the type I boundary operator algebra and the half-sided modular translation structure associated with it. 

In renormalization group (RG) flow, the low energy states form a code subspace that is protected against the local short-distance errors. we will discuss the similarities and differences between this approximate error correction code and the classical and quantum codes that appear in the degenerate vacua of local many-body quantum systems. We will consider continuous MERA as a concrete example and discuss how well the low-energy operators are protected. We will argue that at large N and large gap the approximate error correction code becomes exact.

We analytically compute the quantum field theory entanglement and Renyi entropies of the Dirac fermions on 2 dimensional torus in the presence of background gauge fields. Chemical potential, current source, and topological Wilson loop are unified in a single framework by exhausting all the ingredients of the electromagnetic vertex operators of Zn orbifold conformal field theory. Surprisingly, in infinite space, these entropies become exact and depend only on the Wilson loop. By employing different normalizations for different topological sectors, we manage to get non-singular entanglement entropy. On a circle, we resolve to find the entropies subtly dependent on the chemical potential at zero temperature, which is useful for probing the ground state energy levels of quantum systems.

We consider the backreaction of the winding zero mode on the cigar geometry. We focus on the case of the $SL(2,R)_k/U(1)$ cigar associated with e.g. the near-horizon limit of k NS5 black-branes. We solve the equations of motion numerically in the large k limit as a function of the amplitude of the winding mode at infinity. We find that there is a critical amplitude $A_c=\exp(-\gamma/2)$ that admits a critical solution. In string theory, the exact CFT description of the $SL(2,R)_k/U(1)$ cigar, fixes completely the winding amplitude, $A_s$, at infinity. We find that in the large $k$ limit there is an exact agreement $A_c=A_s$. The critical solution is a cigar with a puncture at its tip; consequently, the black hole entropy is carried entirely by the winding condensate. We comment on the Lorentzian interpretation of the solution.

The revolutionary discovery of gravitational waves has opened an unprecedented experimental window into the Universe. The fact that the relevant physics is often out of equilibrium offers a golden opportunity for holography to make a unique impact on astrophysics and cosmology. I will review recent progress in this direction, with a focus on cosmological phase transitions. In particular, I will describe a recently discovered GW-production mechanism. I will also discuss a new holographic framework to describe strongly coupled matter coupled to dynamical gravity. If time permits, I will briefly mention possible applications to thermal inflation, primordial black holes, (p)reheating, baryogenesis, turbulence, cosmic strings and spacetime singularities. No prior knowledge of string theory or holography required.

The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments

Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this talk, we provide a path integral definition of the volume of the black hole interior and study it at arbitrarily late times for black holes in various models of two-dimensional gravity. Because of a novel universal cancellation between the contributions of the semi-classical black hole spectrum and some of its non-perturbative corrections, we find that, after a linear growth at early times, the length of the interior saturates at a time, and towards a value, that is exponentially large in the entropy of the black hole. This provides a non-perturbative confirmation of the complexity equals volume proposal since complexity is also expected to plateau at the same value and at the same time.