# Fluctuating string in AdS black hole

People frequently use fluctuating string in AdS black hole (see 1,2,3 etc) to study dynamics of a "free external quark" in quark-gluon-plasma (QGP) at finite temperature. The background black hole geometry induces a black hole in the string world sheet. Many interesting results about the boundary theory can be obtained, at least qualitatively, just studying the Nambu-Goto action.

My question is : Why do people usually choose just one of the transverse spatial directions along which the world sheet can fluctuate? Suppose there is a background magnetic field in addition. Shouldn't one need at least two spatial directions for the world sheet to fluctuate to observe/study its effect on the "quark"?

EDIT : Please look at the paragraph just below equation (2.7) in ref-1. The authors are considering only one coordinate namely $x$ which is non-vanishing. This is the only direction along which the string world sheet can fluctuate.

• This was flagged as unclear what you're asking, but given that there are already three references linked in the question what this is about, I'd be interested to hear the reasoning behind it. – ACuriousMind Nov 10 '15 at 14:17
• @ACuriousMind I don't know why it is unclear.. may be I should pin point a region of any of those references which contains my doubt. – Physics Moron Nov 10 '15 at 16:49
• @ACuriousMind I have edited my question. Hopefully this will help in understanding my doubt. – Physics Moron Nov 10 '15 at 16:59