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Significance of non-linear terms

  1. Feb 4, 2009 #1
    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???

  2. jcsd
  3. Feb 4, 2009 #2


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    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?
  4. Feb 4, 2009 #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
  5. Feb 4, 2009 #4
    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!!
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