## SPOCK Mini-conference

At Purdue, we are hosting a mini-conference called SPOCK (Strings and Particles at (Purdue) Ohio, Cincinnati, Kentucky) on Saturday, November 23.

The SPOCK symposia have a long history, and in the past, they have been mostly organized by Philip Argyres:

http://homepages.uc.edu/~argyrepc/homepage/SPOCKlist.html

**Time:** Saturday, November 23, 2019 **Location:** PHY 223.

We meet in room 242 in the physics department for breakfast and the talks will be in room 223.

For local information and more comprehensive travel information please see the visitor’s page.

**Important Parking Information this weekend:** You can park in the Northwestern garage across the physics department for free until 5 pm. However, you must leave the garage by 5 pm because there is a basketball game.

The speakers are

**10:00 – 11:00am Lampros Lamprou (MIT)****11:15 – 12:15am Xinan Zhou (Princeton University)****1:30- 2:30pm Mark Mezei (Simons Center for Geometry and Physics)****2:45 – 3:45pm Nathan Benjamin (Princeton University)**

**“Holographic order from modular chaos”** **Lampros Lamprou**

Abstract: What quantum mechanical principle underlies the emergence of the local geometric structure of the holographic Universe? I will develop a notion of chaos associated with the entanglement pattern of a QFT state by introducing a bound characterizing modular flow of a subregion. In AdS/CFT, a saturation of modular chaos is intimately linked to the local Poincare symmetry and curvature about a bulk Ryu-Takayanagi surface, suggesting an appealing candidate answer to the question posed above.

**“A Basis of Analytic Functionals for CFTs in General Dimension”** **Xinan Zhou**

In this talk, I introduce an analytic approach to the four-point crossing equation in CFT, for the general spacetime dimension. In a unitary CFT, the crossing equation can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis of functions, consisting of double-twist conformal blocks in mean-field theory (and their derivatives with respect to the conformal dimension), in both s- and t-channels. The dual basis is the linear functionals, and I will describe two independent methods to construct them. I will also explain the relation of this work with other analytic approaches, such as the CFT dispersion relation and the Polyakov-Mellin bootstrap.

“**Fine probes of quantum chaos” Mark Mezei**

Quantum chaotic dynamics manifest itself in transport, thermalization, and the butterfly effect. Hydrodynamics is the universal effective description of transport in the long-distance, late time regime. We can gain insight into the process of thermalization from the time evolution of entanglement entropy, for which I introduce an effective theory valid in the hydrodynamic regime. I derive this theory in the special case of holographic gauge theories and present strong evidence for its validity in any chaotic system. I discuss the interplay between this effective theory and chaotic operator growth that is responsible for the butterfly effect, and present new general results on the Lyapunov exponent characterizing this phenomenon. I conclude with some exciting implications for quantum gravity through gauge/gravity duality.

**“Lightcone modular bootstrap and pure gravity” ****Nathan Benjamin**

I will discuss the large spin spectrum of two-dimensional conformal field theories by looking at the modular bootstrap in the lightcone limit. In the presence of a twist gap amongst the Virasoro primary operators (where twist is the difference between conformal dimension and spin), there is a universal expression for the density of states that extends beyond the usual Cardy regime. This expression has an interesting feature which suggests a new upper bound on the lowest twist primary operator present in any 2d CFT. For theories holographically dual to large-radius gravity in AdS$_3$, this new bound is below the BTZ threshold, which in particular would imply that pure AdS$_3$ gravity does not exist.