0
$\begingroup$

Mathematically, in string theory, branes can be described using the notion of a category and the mathematical category theory says that logic can change from one category to another. We can build categories fundamentally described by classical logic, other categories by quantum logic, other categories by intuitionistic logic (e.g topos theory) etc.

Therefore, if branes can be described as objects of a category, couldn't we build models in theoretical physics using branes where these branes would be described by different logics? And if yes, has any renowned physicist done this?

$\endgroup$
2
  • 3
    $\begingroup$ Why branes? Category theory is so general that it describes lots of things in physics. $\endgroup$
    – G. Smith
    Aug 2, 2020 at 17:55
  • $\begingroup$ Basically everything is described by a (higher-) category $\endgroup$ Aug 2, 2020 at 21:46

1 Answer 1

3
$\begingroup$

Clarification: D-branes are defined as categories just in the context of topological string theory. There is no known way to formalize what a D-brane mathematically means in the context of full physical string theory. Also is probably important to recall that while the identification of the B-model branes of a scheme $X$ as the derived bounded category of sheaves of $X$ is fully established (see D-branes, Categories and N=1 Supersymmetry and the wonderful Topological D-branes from Descent ), the connection between the A-model branes and the Fukaya category of $X$ is mostly conjectural and less understood.

Is it possible to use different logic? The answer is not known, as far as my ignorance can tell. But I can argue, from the physics perspective, that the answer is no.

Topological string theory is part of physical string theory, and because of that, it computes relevant physical quantities (F-terms of Calabi-Yau compactifications to be precise, see Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes ). The point is that the structure of string theory is very rigid. All their possible consistent deformation parameters are completely determined by their own dynamical rules. The possibility of a "deformation" is in strong tension with our very basic knowledge of it.

Not to mention that string theory is physics, any alternative description of it must ultimately explain current observations. Even the fact that the very structure of string theory refuses to be reframed could be seen as a prediction that axiomatic systems and other types of logic cannot produce any single useful result for physics, as is actually the case (up to now).

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.