How to switch AC line on and off with a DC control wire
The easiest way is to use a solid state relay. For example, this part from digikey: http://www.digikey.com/product-detail/en/S212S01F/425-2412-5-ND/720407

Then wire it up like the schematic. I used an LED as an indicator so that when the SSR is on, you will know. If you don't need it, then just resize the resistor. The SSR suggests operating at 16mA from the datasheet. 

Assuming arduino is outputting 5V, SSR has 1.4V drop, and LED has 2V drop.

So with LED indicator: 
(5V - 1.4V - 2V)/100 = 16.mA

So without LED indicator: 
(5V - 1.4V)/200 = 18mA







simulate this circuit &ndash; Schematic created using CircuitLab