Re: Nonabelian self-duality
Kea
> When I talked to nonabelian gerbe people about this, one thing they
> said is that it is not clear that in the nonabelian case the
> self-duality should still be ordinary Hodge self-duality, but that it
> might involve in addition to the Hodge star an operation on the Lie
> algebra factor. But I am not quite sure what that should be.
>
> In lack of a better idea, let me assume in the following that we want
> ordinary Hodge duality.....
Once one deals with duality for n-stacks (the only way to look at
quantum general covariance!!) one is in the realm of higher
categorical descent theory and I don't understand that it makes
any sense at all to revert to considerations of a priori metrics and so
on when one has carefully removed this through (very roughly
speaking) the fundamental axiomatisation of topos theory.
Of course, I might be wrong.
Regards
Kea
:smile:
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Urs Schreiber
news:Kea.1j0t...@physicsforums.com...
> Urs Schreiber wrote:
>
>> When I talked to nonabelian gerbe people about this, one thing they
>> said is that it is not clear that in the nonabelian case the
>> self-duality should still be ordinary Hodge self-duality, but that it
>> might involve in addition to the Hodge star an operation on the Lie
>> algebra factor. But I am not quite sure what that should be.
>>
>> In lack of a better idea, let me assume in the following that we want
>> ordinary Hodge duality.....
>
> Once one deals with duality for n-stacks (the only way to look at
> quantum general covariance!!)
Could you explain what you mean by that?
> one is in the realm of higher
> categorical descent theory and I don't understand that it makes
> any sense at all to revert to considerations of a priori metrics and so
> on
The above comment pertained to effective theories of the worldvolume of
5-branes in a limit in which gravity decouples. So there is a fixed
background metric in these contexts, usually even the boring old flat one.
> when one has carefully removed this through (very roughly
> speaking) the fundamental axiomatisation of topos theory.
Hm, not sure what you are referring to here.