# Never go up against a Sicilian

1. Jul 28, 2005

### marcus

this week Laurent Freidel drew the cork on a new bottle of wine and
set out two glasses. He has proposed a toast to (or test of) all approaches: loop and string alike.

It reminded me of some famous words from a comic fairytale called the Princess Bride: never go up against a Sicilian when death is on the line.

This is, however, not the final answer, for there exists an additional term which is usually disregarded. From an effective field theory point of view, this term is as important as the two others, and thus has to be taken into account in the low energy effective action. The corresponding coupling constant is called the Immirzi parameter, $\gamma$. Therefore, the leading bulk terms in the most general four-dimensional low energy gravitational action, in any microscopic quantum theory of gravity (be it string theory, loop gravity etc.) are given by

[equation 4]

...The spectra of the area and volume operators are discrete provided that the Immirzi parameter is not equal to zero. In contrast, there is no indication that area or volume are quantized in string theory (which might be because of the the subtle issue of background independence). Thus any direct experimental constraint of the Immirzi parameter can be taken as concrete steps towards the falsification of a specific microscopic approach. This is the main motivation for the analysis that follows.

he is proposing to loop and string that they each drink the wine of equation (4) and afterwards we can see who keels over. It is a kind of Sicilian roulette. (or if you prefer, Empirical roulette, invented by Francis Bacon circa 1600, back when the English wore ruffles, and were much more Sicilian than they are today.)

Kepler 1571-1630
Bacon 1561-1626
Shakespeare 1564-1616

Although it is a pain in the butt to transcribe equation (4) into LaTex, one of us should so I will.

Oh, the Freidel article is
http://arxiv.org/hep-th/0507253 [Broken]
https://www.physicsforums.com/showpost.php?p=691188&postcount=374

Last edited by a moderator: May 2, 2017
2. Jul 28, 2005

### marcus

Freidel's equation (4)

It is an expression for leading terms in the action, regardless of whichever QG: string, loop or other. Freidel announces that it contains a sicilian term with Immirzality in it. Both glasses contain this term since the wine is the same in both. It is not known whether this number is a finite number (but string dies unless it is zero or infinity and loop dies unless it is somewhere in between).

$$S = -\frac{1}{32\pi G}\int(R^{IJ}\omega \wedge e^K \wedge e^L \epsilon_{IJKL} - \frac{\Lambda}{6}e^I \wedge e^J \wedge e^K \wedge e^L \epsilon_{IJKL} - \frac{2}{\gamma}R^{IJ}\omega \wedge e_I \wedge e_J)$$

the Immirzi term gamma doesnt appear until way at the end :yuck:

Last edited: Jul 28, 2005