The AdS/$\mathsf{C}$-$\mathsf{P}$-${\mathsf T}$ Correspondence

We study the realization of $\mathsf{C}$, $\mathsf{P}$, $\mathsf{T}$ in ${\cal N}=4$ SYM -- corresponding to charge conjugation, parity, and time-reversal -- and identify the $\mathsf{C}$, $\mathsf{P}$, $\mathsf{T}$ global symmetries of ${\cal N}=4$ SYM with bulk (gauge) symmetries of string theory on $AdS_5\times S^5$. The dual bulk transformations are symmetries of Type IIB string theory on $AdS_5\times S^5$ that combine string worldsheet symmetries, with geometric transformations acting on $AdS_5\times S^5$. We show that $\mathsf P$ and $\mathsf T$ map to $\mathsf{CP}$ and $\mathsf{CT}$ under $S$-duality (combined with an $SU(4)$ R-symmetry outer automorphism),while $\mathsf C$ and $ \mathsf{CPT}$ are invariant. We define codimension-two charge conjugation monodromy defects defects in ${\cal N}=4$ SYM, which have an unusual large $N$ expansion, and discuss their bulk dual description. We elucidate the relation between symmetries on the string worldsheet and symmetries of target space string field theory, global vs gauge symmetries in quantum gravity, among related topics. Defects in ${\cal N}=4$ SYM and in quantum gravity play a central role in this work.

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