# Mystery formula

1. Mar 29, 2009

### snoopies622

The UNH Physics Library has equations carved here and there on its walls. So far I recognize every one I've seen except this one:

$$S = \frac {-1}{2 \pi \alpha ' } \int d \tau d \sigma \sqrt { -det (\frac {\partial X ^m}{\partial a} \frac {\partial X_m}{\partial b} ) }$$

The subscript on the second X might be an n instead of another m (I scribbled it hastily and now I can't read my own handwriting) but I'm sure I copied the rest correctly.

What is this?

2. Mar 29, 2009

### isabelle

That looks like a form of the Nambu-goto action, which describes relativistic strings. Look at the last equation:

http://en.wikipedia.org/wiki/Nambu-Goto_action

where the dot and the prime mean partial derivatives with respect to tau and sigma.

It looks like this equation is written in flat minkowski background coordinates, and the subscript on the second X should indeed be an n.

3. Mar 29, 2009

### snoopies622

Yes, that does look about right. I know nothing about string theory so I thought the S was entropy, perhaps. Thanks, Isabelle.