First off, for production you shouldn't be using
(localDB)
- you shoudl be using the actual name of the SQL server instance that your hosting provider has set up for you.
And secondly, attaching a DB is a bad idea in a web environment - you are much, much better off creating the DB in the SQL server instance and referring to that directly.
See here:
Bad habits : Using AttachDBFileName - SQL Sentry[
^]
Thirdly, production should never use integrated security - you should configure a user with exactly sufficient rights to do you application task and no more, and use that to connect instead.
For example, my connection string (with some security changes, obviously) is:
<connectionStrings>
<add name="MembershipDatabase" connectionString="Data Source=www.palm.MyHostingService.com;Initial Catalog=MyMembershipDatabase;Persist Security Info=True;User ID=SMUserName;Password=SMuserPassword"/>
</connectionStrings>