This can be done with Sprout Forms and the Sprout Fields Email Select Field.
The Email Select field allows you to create a dropdown list of email addresses, hides those email addresses on the front-end so they can't be seen or harvested for spam (the user will only see the Name of each department or discipline you wish to have associated with each email address), and makes the selected email address available after the user submits the form so that you can use that value to trigger an email address using Sprout Forms default notifications or Sprout Email Notifications.
As of Sprout Forms v1.1.0 and the current public plugins available (none that I know of for this use case), you can do this with a Dropdown Field.
Let's say you have a dropdown field with the handle
departmentEmailDropdown. In the settings, you can create a list of People/Departments and the emails you'd like them to be sent to:
When a user submits your form, all the values in the form are available for you to reference in your notification settings using shorthand syntax.
In the Email Recipients field of your Notifications tab, you can reference your dropdown field using the syntax
The downsides to this approach are that the email addresses in your dropdown will be visible to in your page template, so robots can swoop in and gobble them up.
We've got this on our radar and in the next couple weeks should have an update for you that will allow you to handle this as well as obfuscate the email addresses on the front-end. I'll update this answer when we have that ready.