Variation of the auxiliary worldsheet metric

  • Thread starter Jack2013
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Can somebody clarify how the formula for variation of the auxilliary worldsheet metric is obtained due to reparametrization of the worldsheet in string theory??
 

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Ben Niehoff
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I could probably explain if I knew which formula you are talking about. Could you type it out, or maybe give a reference to one of the string theory books?
 
  • #3
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In D-branes Clifford J. Johnson page 30 Equation 2.26
 
  • #4
Ben Niehoff
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OK, Clifford is using [itex]\zeta^1, \zeta^2[/itex] to refer to the worldsheet coordinates [itex]\sigma, \tau[/itex]. So the embedding functions are

[tex]X^\mu(\zeta^1, \zeta^2)[/tex]
and the worldsheet metric with "up" indices is

[tex]\gamma^{ab}(\zeta^1, \zeta^2) \frac{\partial}{\partial \zeta^a} \otimes \frac{\partial}{\partial \zeta^b}[/tex]
So, all you need to do is look at the infinitesimal variations of these expressions when you change coordinates

[tex]\zeta^a = \zeta^a(\xi^1, \xi^2)[/tex]
 

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