Non-Unitary Holography

TL;DR

This work extends holography to non-unitary conformal theories based on $U(N+k|k)$ supergroups, showing that to all orders in $1/N$ these theories are indistinguishable from their unitary $U(N)$ counterparts, with differences arising only non-perturbatively as $O(e^{-aN})$. The authors develop the necessary group-theoretic framework, including supertraces and Casimirs $O_p = Str M^p$, and illustrate the non-perturbative distinctions via supermatrix models and localization on $S^4$ for ${ m N}=4$ SYM, where certain Casimir-related operators vanish in $U(N)$ but do not in $U(N+1|1)$. They argue that familiar AdS/CFT setups (Type IIB on $AdS^5 imes S^5$ and M-theory on $AdS^4 imes S^7$) admit non-unitary non-perturbative completions, offering a potential framework for modeling non-unitary black hole evaporation. Overall, the paper suggests a broader landscape for holography that accommodates non-unitary dynamics and prompts reconsideration of unitarity as a strict requirement in holographic dualities, with implications for string theory and quantum gravity.

Abstract

We propose gauge theory/gravity duality involving conformal theories based on U(N+k|k) gauge groups. We show that to all orders in 1/N these non-unitary theories based on supergroups are indistinguishable from the corresponding unitary theories where the gauge group is replaced by U(N). This leads to non-unitary gravity duals which to all orders in 1/N are indistinguishable from their unitary cousins. They are distinguished by operators whose correlation functions differ by O(exp(-aN)). The celebrated type IIB on AdS^5 x S^5 and M-theory on AdS^4 x S^7 fall in this class and thus seem to also admit non-unitary non-perturbative completions. It is tempting to conjecture that this setup may provide a non-unitary model for black hole evaporation.