# String Seminar

## Symmetries and Hilbert Space of Large N Extended States

We discuss the large N expansion in the background of extended states focusing on the

implementation of Goldstone symmetries and the construction of the associated Hilbert space.The large N Thermofield

provides the main focus, with the emergent dynamics of generalized (free) fields and collective symmetry coordinates

## Isometric evolution in de Sitter quantum gravity

Do the postulates of quantum mechanics survive in quantum gravity? The probabilistic interpretation of amplitudes, enforced by the unitarity of time evolution, is not guaranteed within the path integral formulation and has to be checked. Leveraging the gravitational path integral, we find a non-perturbative mechanism whereby a sum over smooth geometries leads to isometric rather than unitary evolution, which we demonstrate in simple models of de Sitter quantum gravity. These models include Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant. In these models we find that knowledge of bulk physics, even on arbitrarily large timescales, is insufficient to deduce the de Sitter S-matrix.

## Ground State Entanglement in Long-Range Systems

I will talk about our work investigating the scaling of entanglement entropy in ground states of long-range systems. We study free fermionic lattice models in one-spatial dimension where the hopping and pairing terms decay as a power law with exponent α. In disordered models, we find fractal scaling of entanglement approaching a volume-law as α goes to zero. In models with a continuum limit, the scaling is constrained by predictions from the low-energy theory. There is no universality in the critical α beyond which area-law scaling of local systems is restored. These features are expected to persist in more general system

## Symmetry TFTs of 4d N=3 SCFTs

We review the notion of the 5d symmetry topological field theory (TFT) of a 4d quantum field theory (QFT), and try to apply it to N=3 superconformal field theories (SCFTs).

## Bootstrap bounds on D0-brane quantum mechanics

I derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski’s virial theorem bound to finite energies and gives the first non-trivial bound on 〈TrX2〉. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. The best lower bounds are already a factor of ~ 0.7 from the large N extrapolation of Monte Carlo predictions.

## Emergent Area Laws from Entangled Matrices

Arguments such as those due to Susskind and Uglum show that open strings ending on an entangling surface are crucial to understanding the nature of black hole microstates in string theory and the degrees of freedom being partitioned by Ryu-Takayanagi surfaces in holography. We seek an understanding of these edge modes from the perspective of the boundary theory.

In this talk, we will focus on a particular Matrix Quantum Mechanics model known as mini-BMN that describes an emergent noncommutative Yang-Mills theory on a fuzzy sphere. In mini-BMN and similar models, an analogous problem involves correctly treating the off-diagonal matrix elements that connect eigenvalues on either side of the entanglement cut. We show that these operators, which may be thought of as open strings stretching between D0-branes on either side of the cut, carry representations under the theory's SU(N) symmetry which store information about the size of the entangling surface in the emergent geometry.

## CFT Dual of $dS_3$ and Pseudo Entropy

We propose a holographic duality for gravity on a three-

dimensional de Sitter space. This is essentially given by a $k=-2$ limit

of SU(2) WZW model. We show that this proposal reproduces the expected

free energy in de Sitter gravity. We also analyze the geodesic length in

the three dimensional de Sitter spacetime and argue that it is

interpreted as holographic pseudo entropy. We will also discuss a time-

like entanglement entropy in AdS/CFT which shares a similar property in

terms of pseudo entropy.

Zoom link will be posted shortly before the seminar.