Computer systems designers are building cache hierarchies with higher capacity to capture the ever-increasing working sets of modern workloads. Cache hierarchies with higher capacity improve system performance but shift the performance bottleneck to address translation. We propose Midgard, an intermediate address space between the virtual and the physical address spaces, to mitigate address translation overheads without program-level changes. Midgard leverages the operating system concept of virtual memory areas (VMAs) to realize a single Midgard address space where VMAs of all processes can be uniquely mapped. The Midgard address space serves as the namespace for all data in a coherence domain and the cache hierarchy. Because real-world workloads use far fewer VMAs than pages to represent their virtual address space, virtual to Midgard translation is achieved with hardware structures that are much smaller than TLB hierarchies. Costlier Midgard to physical address translations are needed only on LLC misses, which become much less frequent with larger caches. As a consequence, Midgard shows that instead of amplifying address translation overheads, memory hierarchies with large caches can reduce address translation overheads. Our evaluation shows that Midgard achieves only 5% higher address translation overhead as compared to traditional TLB hierarchies for 4KB pages when using a 16MB aggregate LLC. Midgard also breaks even with traditional TLB hierarchies for 2MB pages when using a 256MB aggregate LLC. For cache hierarchies with higher capacity, Midgard's address translation overhead drops to near zero as secondary and tertiary data working sets fit in the LLC, while traditional TLBs suffer even higher degrees of address translation overhead.