Brane fluctuations via $S$-duality

Question

Caveat lector: I'm a mathematician trying to learn physics so I apologize if my questions are very vague or trivial.

I'm currently studying Maldacena's Black Holes in String Theory (https://arxiv.org/abs/hep-th/9607235) and I want to understand better an example given in Section 1.3. It concerns the interpretation given to massless open strings attached to a brane (in the type IIB theory I believe). It's asserted that when the vector index of the open strings are in the transverse directions to the brane, they represent fluctuations of the brane in those directions. My goal is to understand this more precisely, particularly with the example given therein.

One takes a D-string wrapped once around a compact dimension and in turn there can be now (a gas of?) open strings attached to the D-string. Now comes the part I can't understand. Applying S-duality in this context this configuration get's pictured as a fundamental string along the same direction in wich the D-string wrapped,with a different tension. Is this final line correct? As the picture is that of a fundamental string with changed tension I interpret it as excited or having suffered some oscilation.

Along this line he considers a gas of open strings and states

The energy of a D-brane containing a gas of open strings is $$ E= \frac{R_9}{\alpha'g}+ \sum_i \epsilon_i = E_0+ \frac{N_L+N_R}{R_9} $$

How is this equation (both equalities) derived? What are the $\epsilon_i$?. I can't understand it in the paper.

Also I can't understand in wich "stage" S-duality is applied, if with the gas of open strings included to finally give the excited superstring in the S-dual picture.

This post imported from StackExchange Physics at 2022-01-03 10:46 (UTC), posted by SE-user Rebour

Comments

Susskind talks about S-duality between D-string and F-string at around 27:00 youtube.com/watch?v=NZ-ElsvYKyo

This post imported from StackExchange Physics at 2022-01-03 10:46 (UTC), posted by SE-user Mitchell Porter

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Thank you, this I found a nice intuition for some parts of S-duality but it's far from, tough, helping me understand the picture more precisely. If nobody answers and I find something I will post it as an answer myself

This post imported from StackExchange Physics at 2022-01-03 10:46 (UTC), posted by SE-user Rebour