Speaker
Description
The late time behaviour of $\mathrm{OTOC}$s involving generic non-conserved local operators show exponential decay in chaotic many body systems. However, it has been recently observed that for certain holographic theories, the $\mathrm{OTOC}$ involving the $U(1)$ conserved current for a gauge field instead varies diffusively at late times. The present work generalizes this observation to conserved currents corresponding to higher-form symmetries that belong to a wider class of symmetries known as generalized symmetries. We started by computing the late time behaviour of $\mathrm{OTOC}$s involving $U(1)$ current operators in five dimensional AdS-Schwarzschild black hole geometry for the 2-form antisymmetric $B$-fields. The bulk solution for the $B$-field exhibits logarithmic divergences near the asymptotic AdS boundary which can be regularized by introducing a double trace deformation in the boundary CFT. Finally, we consider the more general case with antisymmetric $p$-form fields in arbitrary dimensions. In the scattering approach, the boundary $\mathrm{OTOC}$ can be written as an inner product between asymptotic 'in' and 'out' states which in our case is equivalent to computing the inner product between two bulk fields with and without a shockwave background. We observe that the late time $\mathrm{OTOC}$s have power law tails which seems to be a universal feature of the higher--form fields with $U(1)$ charge conservation.
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