February 13, 2007

Primer

I’ve been reading Michael Dine’s new book, Supersymmetry and String Theory: Beyond the Standard Model.

Since any one of the phrases in the title could well be (and has been) the subject of a multi-volume opus, it comes as somewhat of a surprise that the entire book weighs in at a mere 503 pages.

This gives, in places, a whirlwind feel to the book. An extreme example is the chapter on General Relativity. In 15 pages, Dine introduces general coordinate transformations, derives the Christoffel symbols, discusses the Riemann curvature tensor and its symmetries, derives the Schwarzschild solution as the most general static, isotropic solution to the vacuum Einstein equations, introduces Bekenstein and Hawkings results on the thermodynamics of blackholes, and still has a page left over to discuss the coupling of spinors to gravity.

Another more minor example is his discussion of Grand Unification. He correctly notes that unification works better with supersymmetry than without it. To drive home the point, he presents non-supersymmetric Grand Unification in the maximally unflattering light (run $\alpha_1,\alpha_2$ up to the point where they unify, then run $\alpha_3$ down to the $Z$ mass, where it is 7 orders of magnitude off). The naïve reader might be forgiven for wondering why anyone ever thought of non-supersymmetric Grand Unification in the first place.

But these are minor quibbles. My only real complaint is that this book stops just short of where someone with an interest in String Theory and beyond-the-Standard Model physics would like to be taken. I think that one would want, in such a book, a discussion of the leading candidates for bridging the gap: heterotic M-theory and Type-IIB orientifolds with fluxes.

These get very brief mention (respectively, in section 28.7, where it is explained that heterotic M-theory solves the “Dine-Seiberg problem,” and in the “Coda,” where we are introduced to the “landscape”), But the presentation of Randall-Sundrum, in chapter 29, would be much improved by an explanation of the warped nature of the typical heterotic M-theory and, even moreso, by a mention of the large warpings that can arise in IIB flux compactifications. More generally, a discussion of these contemporary efforts at string phenomenology would provide an opportunity to tie the last part of the book more closely together with the considerations of the first 300 pages.

Still, there’s a wealth of information here, for the beginning graduate student (a solid course in Field Theory, and a rudimentary acquaintance with the Standard Model are a prerequisite), and nuggets of insight that will satisfy the seasoned researcher. The chapters on supersymmetry and cosmology are especially good.

I would say that this book belongs on the bookshelf of any (aspiring) high energy theorist. But perhaps the bedside table would be an even better location.

Posted by distler at February 13, 2007 1:52 AM

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Re: Primer

What is the Dine-Seiberg problem?

Posted by: Tim on February 13, 2007 9:28 AM | Permalink | Reply to this

Re: Primer

Very crudely, 4D physics is characterized by 3 parameters:

1. The 4D Planck mass, $M_{\text{pl}}$.
2. The 4D GUT scale, $M_{\text{GUT}}$.
3. The GUT coupling, $\alpha_{\text{GUT}}$.

The string compactification is (again, very crudely) also characterized by 3 parameters

1. $\alpha'$.
2. $g_s$.
3. $V$, the volume of the 6-manifold on which you compactified.

For any given class of compactifications, you can express one set of parameters in terms of the others. So … take (say) a weakly-coupled heterotic string compactification, and express $\alpha'$, $g_s$ and $V$ in terms of $M_{\text{pl}}$, $M_{\text{GUT}}$ and $\alpha_{\text{GUT}}$, using the formulæ appropriate to this class of compactifications. Now plug in the observed values of $M_{\text{pl}}$, $M_{\text{GUT}}$ and $\alpha_{\text{GUT}}$. What you find is that, contrary to your starting assumptions, the computed value for $g_s$ is not small. So it was not self-consistent to assume that you were in a weakly-coupled heterotic string background.

That’s the Dine-Seiberg problem.

Posted by: Jacques Distler on February 13, 2007 10:48 AM | Permalink | PGP Sig | Reply to this

Re: Primer

Apparently, a new book called String Theory in a Nutshell is scheduled to be released later this year.

Posted by: Tim on February 13, 2007 9:39 AM | Permalink | Reply to this

Re: Primer

Wondering why this would fit into O’Reilly’s series and which animal would be on the cover, I looked it up. Contrary to what I imagined, it seems to be a solid introductory book by Elias Kiritsis. I’ll wait for Jacques’ review in May 2007…

Posted by: Volker Braun on February 13, 2007 10:14 AM | Permalink | Reply to this

Re: Primer

It looks like Princeton UP is starting a new “In a Nutshell” series, with Astrophysics (D. Maoz), Nuclear Physics (C. Bertulani) and String Theory (E. Kiritsis) all due out in a few months. I suppose they’re following on Anthony Zee’s QFT book.

Posted by: Blake Stacey on February 15, 2007 2:17 PM | Permalink | Reply to this

Re: Primer

I am curious if you think the Dine book ‘Supersymmetry and String Theory’
is related to a publication from the editors of Cambridge Monographs on Mathematical Physics:

Terry Gannon, ‘Moonshine beyond the Monster’?

Posted by: Doug on February 14, 2007 12:45 PM | Permalink | Reply to this

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