## August 16, 2004

### Escape from the Fog

#### Posted by Urs Schreiber

We went by train to Andenes/Norway, the most norther spot on the Vesteralen island group where the European continental plate drops off sharply enough that sperm whales, which are the incarnation of the idea of deep sea diving, can be spotted within a ship-hour distance from the shore.

With due stops in Berlin and Stockholm such a trip takes about 55 hours but can be spent leisurely in the armchair of a lounge waggon with a glass of wine and the endless swedish landscape passing by.

Without really noticing how it happend I thus found myself thinking about super-Pohlmeyer invariants and boundary states for non-abelian gauge fields. There was something I still didn’t quite understand. But some sort of fog prevented me from seeing clearer.

But after crossing the norwegian border I was called back to reality as the woods gave way to a dramatic Fjord landscape, dropping off almost vertically right next to the rails.

As then the bus took us through Slartibartfast’s award-winning design from Narvik over the Lofoten to Andenes I began finally to see the fog, creeping in like a living being.

It covered Andenes like a blanket and when I fell to sleep in a midsummer-lit grey soup in our cabin it truly felt like the end of the world.

After an eventful next day the bright midsummer night inspired us to rent bikes and try to get out of that blanket. What an experience. Behind a tiny tunnel through the rocks 5 km south of Andenes neir Bleik, the fog ended as if cut through and a meditarranean beach lay in front of us, shone on by a low-hanging sun.

And - believe it or not - the fog in my mind lifted, too, and suddenly I was seeing clearly:

When the transversal components of the gauge field $A$ mutually commute, the super-Pohlmeyer invariant constructed from that $A$ becomes equal to the boundary deformation operator considered in hep-th/0407122. Furthermore, the condition for the ‘analytic’ extension of the super-Pohlmeyer invariant restricted to the sub-phase-space where $R$ is invertible is invariant if the longitudinal excitations are in light cone gauge.

(If anyone wants to know what this gibberish means, have a look at these notes.)

When we awoke next day the fog over Andenes was gone and we had a great couple of days watching whales, reading Moby Dick, learning about whales in the local whale museum, having apply pie and coffee at midnight in the everlasting afternoon, travelling on the Hurtigrute, almost swimming in the sea - and playing the wind harp.

Posted at August 16, 2004 7:09 PM UTC

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