Unquenched Flavor in the Gauge/Gravity Correspondence

Table 1

The two classes of leading UV behaviors.

𝑁𝑓	I	II
<2𝑁𝑐	𝑃∼𝑄∼|2𝑁𝑐−𝑁𝑓|𝜌
	𝑒^2ℎ∼12(2𝑁𝑐−𝑁𝑓)𝜌
	𝑒^2𝑔∼𝑁𝑐
	𝑁𝑌∼^𝑐4
	𝑒^4(𝜙−𝜙𝑜)∼𝑒^4(𝜌−𝜌𝑜)sinh^2(2𝜌𝑜)2𝑁^2𝑐(2𝑁𝑐−𝑁𝑓)𝜌
	2𝑎∼𝑁𝑐(2𝑁𝑐−𝑁𝑓)𝑒^−2(𝜌−𝜌𝑜)𝜌
>2𝑁𝑐	𝑃∼−𝑄∼|2𝑁𝑐−𝑁𝑓|𝜌	𝑃∼𝑐+𝑒^4𝜌/3
	𝑒^2ℎ∼14(𝑁𝑓−𝑁𝑐)	𝑒^2ℎ∼14𝑐+𝑒^4𝜌/3
	𝑒^2𝑔∼12(𝑁𝑓−2𝑁𝑐)𝜌	𝑒^2𝑔∼𝑐+𝑒^4𝜌/3
	1𝑌∼4(𝑁𝑓−𝑁𝑐)	1𝑌∼6𝑐+𝑒^4𝜌/3
	𝑒^4(𝜙−𝜙𝑜)∼𝑒^4(𝜌−𝜌𝑜)sinh^2(2𝜌𝑜)2(𝑁𝑐−𝑁𝑓)^2(𝑁𝑓−2𝑁𝑐)𝜌	𝑒^4(𝜙−𝜙𝑜)∼1
	𝑎∼𝑒^−2(𝜌−𝜌𝑜)𝜌	𝑎∼2𝑒^−2(𝜌−𝜌𝑜)
=2𝑁𝑐	𝑃∼𝑁𝑐+𝑁^2𝑐+𝑄^2𝑜∼8𝑁𝑐(4−𝜉)𝜉
	𝑒^2ℎ∼𝑁𝑐𝜉
	𝑒^2𝑔∼4𝑁𝑐4−𝜉
	𝑁𝑌∼^𝑐4
	𝑒^4(𝜙−𝜙𝑜)∼𝑒^4(𝜌−𝜌𝑜)sinh^2(2𝜌𝑜)(4−𝜉)𝜉16𝑁^3𝑐
	4𝑎∼𝜉𝑒^−2(𝜌−𝜌𝑜)