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v3.3.2-pre
I will review how AdS-CFT rephrases certain questions in specific quantum field theories in terms of a dual geometric problem. This allows techniques in geometry to be applied which may yield new constraints and results governing the physics of these theories. We explore these ideas giving some examples, and emphasising their power in the case the field theory is put on a curved spacetime. We will discuss bounds on the energy gap when these theories are confining. In the 2+1 case, we will discuss a result that implies the Casimir energy is always non-positive when the theory is put on a curved space. And again in 2+1 I will describe a bound on entanglement entropy that applies in rather general situations. I will then discuss to what extent these results may constrain the behaviour of more general (non-holographic) theories.