Can I break my lease if my job transfers me?

To start, you need to read your lease. There may be language that addresses this issue. If not, then you are not entitled you to terminate your lease which means that you are still liable for the remaining rent. However you should be aware that, your landlord is under a duty to "mitigate damages" after you move out. What this means is that they must use reasonable efforts to find a new tenant. If, and when, that happens you will then be relieved of any further financial obligation.
 
In order to move things along, perhaps you know of someone who would like take over your space. Also, ask if you can sublet your unit. In a sublet you in effect become the "landlord" or techically "sublandlord". Then, you could charge the subtenant less than what you are paying but it would at least give you some rent relief. However, you would need your landlord's permission to do so and, with a sublease, you will still remain liable for the rent if your subtenant fails to pay.
 
Finally, check with your employer to see if it can help offset some of your rental expenses through a relocation allowance. Many companies will do this.