Abstract
AbstractBMN Matrix theory admits vacua in the shape of large spherical membranes. Perturbing around such vacua, the setup provides for a controlled computational framework for testing information evolution in Matrix black holes. The theory realizes excitations in the supergravity multiplet as qubits. These qubits are coupled to matrix degrees of freedom that describe deformations of the spherical shape of the membrane. Arranging the ripples on the membrane into a heat bath, we use the qubit system as a probe and compute the associated Feynman-Vernon density matrix at one loop order. This allows us to trace the evolution of entanglement in the system and extract the characteristic scrambling timescale. We find that our numerical analysis is consistent with this time scaling logarithmically with the entropy of the qubit system, in tune with suggestions by Sekino and Susskind.
Highlights
Models have been developed in the literature [6, 7], but none that are related to black holes or gravitational dynamics, let alone being realized within string theory
In [15], it was shown that, for the vacuum of BMN theory corresponding to a single spherical M2 brane with N units of light-cone momentum, the perturbation dynamics can be mapped onto the dynamics of 8 N 2 qubits coupled to 3 N 2 bosonic variables that describe the shape of the M2 brane
Given the connections fast scrambling has to black hole dynamics [4, 5, 7, 36], our result is further circumstantial evidence that BMN Matrix theory is a theory of quantum gravity
Summary
For weak coupling g 1, the fermionic sector consists of 8 N 2 qubit coupled to the bosonic sector through the LBF F term. We consider the limit of small coupling constant g 1 and large N 1 In this small g regime, our leading order computation amounts to considering the schematic Feynman diagrams shown in figure 2. Connections between the qubits, and the question we are to address is whether this high density of connections is enough to lead to fast scrambling of qubit information. In this regard, note that entanglement can only be generated by a boson-fermion-fermion vertex since this is the only dynamical mechanism for flipping and entangling qubits. There is no direct scrambling at a work in the last two diagrams of figure 2(a)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
