Butterfly Effect and Holographic Mutual Information under External Field and Spatial Noncommutativity

Understand

We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to a stack of N black M-branes to find the Melvin spacetime of a stack of N black D-branes with magnetic or electric flux in string theory, after the Kaluza-Klein reduction.

• We slightly extend previous formulas to investigate the external magnetic and electric effects on the butterfly effect and holographic mutual information.
• It shows that the Melvin fields do not modify the scrambling time and will enhance the mutual information.
• In addition, we also T-dualize and twist a stack of N black D-branes to find a Melvin Universe supported by the flux of the NSNS b-field, which describes a non-comutative spacetime.