Exploring supersymmetric wormholes in $\cal{N} = 2$ SYK with chords

TL;DR

This paper investigates supersymmetric wormholes in the $ ext{N}=2$ SYK model, revealing their ground state structure, computing wavefunctions, and uncovering enhanced supersymmetry in the transfer matrix, with implications for black hole physics.

Contribution

It introduces improved super-chord Hilbert space construction, computes the zero-temperature Hartle-Hawking wavefunction, and demonstrates an $ ext{N}=4$ supersymmetry in the wormhole transfer matrix.

Findings

Reproduces ground state count with non-perturbative corrections

Shows enhanced $ ext{N}=4$ supersymmetry in the transfer matrix

Provides explicit expressions for zero-temperature two-point functions

Abstract

A feature the $\mathcal{N}=2$ supersymmetric Sachdev-Ye-Kitaev (SYK) model shares with extremal black holes is an exponentially large number of ground states that preserve supersymmetry. In fact, the dimension of the ground state subsector is a finite fraction of the total dimension of the SYK Hilbert space. This fraction has a remarkably simple bulk interpretation as the probability that the zero-temperature wormhole -- a supersymmetric Einstein-Rosen bridge -- has vanishing length. Using chord techniques, we compute the zero-temperature Hartle-Hawking wavefunction; the results reproduce the ground state count obtained from boundary index computations, including non-perturbative corrections. Along the way, we improve the construction [arXiv:2003.04405] of the super-chord Hilbert space and show that the transfer matrix of the empty wormhole enjoys an enhanced $\mathcal{N} = 4 $ supersymmetry. We also obtain expressions for various two point functions at zero temperature. Finally, we find the expressions for the supercharges acting on more general wormholes with matter and present the superchord algebra.