Polyakov Definition and 9 Threads

Recently I've came to some references on mathematical aspects on string theory that deal with the Polyakov euclidean path integral. An example is the book "Quantum Fields and Strings: A Course for Mathematicians. Volume 2", where it is stated roughly that the path integral is $$A =...

In the notes of Arutyunov, he writes down the equation of Polyakov action in what he calls a first-order formalism(equation 3.19). But here I did not understand how he got this equation. Can someone help? Moreover, can someone explain how he got the constraints in equation 3.25? And why they...

General physical perturbations of string is derived by A.Larsen and V.Frolov (arXiv:hep-th/9303001v1 1March 1993). An arbitrary string configuration is in 4-dimensional gravitational background. Starting point is Polyakov action $$ S = \int d \tau d\sigma \sqrt {-h} h^{AB} G_{AB}$$. Here is...

The Polyakov action is invariant under Weyl transformations, that is local rescaling of the metric tensor on the world sheet. However, I don't really understand the physical meaning of this. What would it mean for the action to not have this symmetry? I also have another question concerning...

The Polyakov action, S=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-h}h^{\alpha\beta}G_{ij}(X)\partial_\alpha X^i\partial_\beta X^j has the local symmetries, diffeomorphism on world sheet and the Weyl invariance. But is diffeomorphism on the target space also a symmetry? The target space...

[SOLVED] Diffeomorphism invariance of the Polyakov action Hi, I'm struggling with something that is quite elementary. I know that the Polyakov action is diffeomorphism invariant and Weyl invariant. Denoting the world-sheet coordinates \sigma^0 = \sigma and \sigma^1 = t and the independent...

According to 't Hooft - Polyakov monopole solution, SO(3) is spontaneously broken down to U(1) and the unbroken mode works very well as the electromagnetic field. In this case we do not need dirac string but just some scalar field. At very large distance , the two massive gauge modes can be...

I ran across the following passage in the Wikipedia article on mass-energy equivalence: This level of physics is way over my head, but I'm wondering: "What happens to the quarks that comprise the protons and neutrons?" Are they conserved in the neutrinos and antielectrons? Chris

Hi there, I 've recently looked at how the Nambu-Goto action of an open string can be derived from the proper area of the parameterised world-sheet, in the form of either the derivatives of space-time coordinates or the determinant of the induced metric. However, may I ask what are the...