Significance of non-linear terms

In summary, the conversation discusses the potential significance of adding non-linear terms to the action in string theory, specifically in the context of string cosmology. The addition of such terms, such as the self-linking number in the Nambu-Goto formalism, may affect the compact extra dimensions and potentially have implications for the Landscape. The relevance of these terms in string-inspired cosmology is also mentioned.
  • #1
anuradha
4
0
hi,
Do the addition of non-linear terms in action play any significant role in string theory??
if so, what is its significance in string cosmology?

---
anuradha
 
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  • #2
Are you talking about the action of the fundamental strings, or about the action of low-energy effective field theory that results from string theory?
 
  • #3
Dear anuradha,

Well the Nambu-Goto action is itself non-polynomial - because of the square-root. In the Nambu-Goto formalism, there is a topological term that we can add - the self-linking number. It is non-linear. But I have never seen a quantisation of the Nambu-Goto action with this knot theory topological term included.

On the other hand, I am not aware of any such topological term constructed from the X^mu, that measures knottedness in the Polyakov framework. Presumably if such a term exists - then it must be non-linear.

I would expect such terms to affect the compact extra dimensions because such terms imply highly non-trivial world-sheet topology and one must use the theory of Algebraic Surfaces and NOT merely Riemann Surfaces.

From the cosmology point of view - a new constraint on the compact extra dimensions will make the Landscape smaller...

Best Regards
Alwi
 
  • #4
Demystifier said:
Are you talking about the action of the fundamental strings, or about the action of low-energy effective field theory that results from string theory?
thank you for your reply.
let me make it more clear!
see for eg: if the action is S=int{d^4x*(L_d+k*L_d^2)}, where L_d characterises the lagrangian density of the fermionic field and k being some constant(to make correct dimensionality)...by adding L_d^2 , S contains a non-linear term, right?
i am talking about such a field...does it hold any physical significance to string cosmology??
or does the L_d^2 term belong to string inspired cosmology??if so what may be its relevance??


hope you got my question!
-anuradha
 

Related to Significance of non-linear terms

1. What are non-linear terms and why are they significant?

Non-linear terms are mathematical expressions that involve powers, products, or other operations on the variables in a model. They are significant because they allow for more complex and realistic relationships between the variables, which can better capture the true nature of a phenomenon.

2. How do non-linear terms affect the interpretation of a model?

Non-linear terms can greatly impact the interpretation of a model by introducing curvature and interactions between variables. This means that the effect of one variable on the outcome may depend on the value of another variable, making it important to carefully examine the relationships between variables in the model.

3. Can non-linear terms improve the accuracy of a model?

In some cases, adding non-linear terms to a model can improve its accuracy by allowing for a better fit to the data. However, this is not always the case and the choice to include non-linear terms should be based on the specific research question and the data at hand.

4. Are there any assumptions associated with using non-linear terms in a model?

Yes, there are several assumptions that should be considered when using non-linear terms in a model. These include the assumption of linearity, which states that the relationship between the variables is not too complicated, and the assumption of normality, which states that the errors in the model are normally distributed.

5. How do I know if I should include non-linear terms in my model?

The decision to include non-linear terms in a model should be based on a combination of statistical tests and subject-matter expertise. It is important to assess the significance and practical implications of the non-linear terms, as well as consider if they align with prior knowledge and theories about the variables being studied.

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