Cosmic F- and D-strings

December 17, 2003

Posted by Urs Schreiber

In the paper

Copeland, Myers, Polchinski, Cosmic F- and D-strings

the authors discuss cosmic strings and F/D-strings on the same footing. I am not sure that I completely understand how the transition from the quantum realm of the F-strings to the classical realm of cosmic strings is performed. Is it sufficient to just mumble “string-string and string-field dualities?”

For instance, when the authors say that experimental observation of cosmic strings might shed light on stringy physics, are they referring to the general “(classical) physics described by Polyakov-type actions” or do they really mean to imply that the observation of cosmic strings would tell us anything about (F-)string scale physics?

Posted at December 17, 2003 10:15 PM UTC

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Re: Cosmic F- and D-strings

I’m not sure what you are surprised about. A “macroscopic” fundamental string is a string with large occupation numbers for certain string modes. That’s more-or-less exactly the situation in which one gets classical behaviour.

Posted by: Jacques Distler on December 18, 2003 12:54 AM | Permalink | Reply to this

Re: Cosmic F- and D-strings

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Hm, I’d thought that when you pump so much energy into a fundamental string as to make it macroscopically long, you create a black hole, as evidenced by the string/black hole correspondence principle, e.g.

Damour, Veneziano, Self-gravitating fundamental strings and black-holes

which goes back to

Horowitz, Polchinski, A Correspondence Principle for Black Holes and Strings.

In particular the string contracts under its own gravity to produce a “string ball”, e.g.

Cheung, Black hole, string ball, and $p$ -brane production at hadronic supercolliders.

Posted by: Urs Schreiber on December 18, 2003 12:10 PM | Permalink | Reply to this

Re: Cosmic F- and D-strings

First of all, the above statement held also in the free string (vanishing string coupling), in which case, of course, there are no black holes.

Second, whether something is a blackhole is a global property. We are talking about cosmic strings — strings stretched across the cosmological horizon. If such a string is a blackhole, we can’t tell … yet.

Posted by: Jacques Distler on December 18, 2003 1:47 PM | Permalink | Reply to this

Re: Cosmic F- and D-strings

Ok, I see your point and of course I agree. Maybe my initial question was phrased improperly.

Surely I understand how to take the classical limit of a quantum system and that high excitation numbers of the string will make a classical approximation possible. (In particular the entire string/black hole correspondence can be derived from such purely classical reasoning, which approximates the highly excited string by a random walk).

But: The quantum nature of the fundamental string has further implications that have no counterpart in non-fundamental macroscopic string-like objects. Most prominently, quantization fixes the number of spacetime dimensions. Maybe my original question becomes clearer when expressed as follows:

Would the detection of cosmic strings (which, according to Copeland, Myers, and Polchinski, would provide a window into “stringy” physics) imply that there are 10 spacetime dimensions?

This is what I mean when asking about the classical/quantum relationship in cosmic/fundamental strings. Everybody agrees that the classical dynamics of a cosmic string (a huge linear defect of some sort) is to a good approximation described by a Nambu-Goto/Polyakov action (whichever). We know that consistently quantizing this action leads to a set of interesting constraints. But would the detection of cosmic strings convince string-critics that these constraints are laws of nature? Wouldn’t they much rather argue that the cosmic string is not fundamental and hence its effective action shouldn’t be quantized the strict way it is for the fundamental string?

Sorry if this should sound confused. Maybe I just have to get used to the idea, which may be obvious to you, that cosmic strings and fundamental strings can be handled on the same footing.

Posted by: Urs Schreiber on December 18, 2003 4:54 PM | Permalink | Reply to this

Re: Cosmic F- and D-strings

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I should admit that I haven’t looked at any of those papers, but $\ldots$

Maybe this is more in the spirit of your question: Jacques suggests taking a string with some large occupation number, for example one in which the $\alpha_1$ oscillator is highly excited so the radius becomes macroscopic or even of cosmological scale. Of course this is an exact solution to the free string equations of motion but the question is whether this behaves as a macroscopic string. For this remember that the tension is given by the string scale so it has costed you a lot of energy to pull it that long and it will be very stiff.

Furthermore, what happens if you perturb it a little bit? Does it stay macroscopic or does its selfgravity (and other long range forces) let it collapse and and turn this exact solution unstable?

I always thought that cosmic strings (the ones of cosmology, not those of F-theory) are a moduli space approximation of some theory that has vortex solutions, for example $U(1)$ with a scalar with a mexican hat potential. There you impose boundary conditions that make the scalar wind around the hat and thus in a central line the scalar field has to go “over the top” of the potential.

Hence, you have potential energy localized along a line and the low energy excitations behave like a string. But as this is only a low energy approximation you wouldn’t expect to obey your quantum consitency conditions (like critical dimension etc).

This is like nuclear physics where you can have arbitrary spin nuclei that can evade the no-go theorems about higher spin theories because they are composite.

Posted by: Robert on December 19, 2003 8:05 AM | Permalink | Reply to this

Re: Cosmic F- and D-strings

You precisely address my concern when you say:

But as this is only a low energy approximation you wouldn’t expect to obey your quantum consitency conditions.

With respect to this the authors of that paper write in their introduction:

Before the ‘second superstring revolution’ there appeared to be a clear distinction between fundamental strings and cosmic strings. […] Today the situation in string theory is much richer […] the various string-string and string-field dualities relate these objects to each other, and to the field theoretic flux tubes, so that they are actually the same object as it appears in different parts of the parameter space.

P.S.
On a technical note: I tried to use the ‘blockquote’ command in the above, but it always produces a validator error message. How does one quote correctly in this blog?

Posted by: Urs Schreiber on December 19, 2003 6:42 PM | Permalink | Reply to this

Blockquotes

In XHTML, blockquotes need to contain “block-level”, rather than “inline” material. So you would write

<blockquote><p>This is a blockquote, where the quoted material is wrapped in a paragraph element.</p></blockquote>

Instead of <p>, you could use other block-level elements (like, say <pre>), or you could have more than one paragraph, etc. (If you want more than one paragraph, in a blockquote, though, I’d suggest turning off the “Convert Linebreaks” option, as it’s pretty tricky to get the desired set of XHTML tags to come out with that option turned on.)

Posted by: Jacques Distler on December 19, 2003 6:57 PM | Permalink | Reply to this

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December 17, 2003