A holographic inequality for N=7 regions

In holographic duality, boundary states that have semiclassical bulk duals must obey inequalities, which bound their subsystems' von Neumann entropies. Hitherto known inequalities constrain entropies of reduced states on up to N = 5 disjoint subsystems. Here we report one new such inequality, which involves N = 7 disjoint regions. Our work supports a recent conjecture on the structure of holographic inequalities, which predicted the existence and schematic form of the new inequality. We explain the logic and educated guesses by which we arrived at the inequality, and comment on the feasibility of employing similar tactics in a more exhaustive search.

Automated summary

In holographic duality, semiclassical bulk duals of boundary states are subject to inequalities that restrict the von Neumann entropies of their subsystems. Existing inequalities only apply to up to N = 5 disjoint subsystems, but we have discovered a new inequality involving N = 7 disjoint regions. Our findings support a recent conjecture on the structure of holographic inequalities and provide insights into the potential for further exploration using similar tactics.