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B Metric for Calabi-Yau manifolds dynamic?

  1. Mar 31, 2017 #1
    Are the metrics for say the Calabi-Yau manifolds of string theory, assuming they have a metric, dynamic in the sense that a vibrating string interacts with the compact space causing the metric to change where there is a string, even if only a tiny amount?

  2. jcsd
  3. Apr 1, 2017 #2
    Yes, the Calabi-Yau metric would be dynamical, and the gravitational effects of a string will be similar to what I wrote about electromagnetism in string theory. In a quantum field theory of gravity, the metric is a quantum field whose quanta are the gravitons, and the metric values correspond to density of virtual gravitons. A string can emit graviton-strings (which must be closed strings, unattached to any brane), and it therefore has a gravitational field, i.e. an effect on the metric.

    We can distinguish between the gravitational field in the 3+1 large dimensions, and the gravitational field in the small compact dimensions, though in both cases it all comes from virtual gravitons. In the large dimensions, that's just gravity as we're familiar with it. In the compact dimensions... the Calabi-Yau can certainly change. There are two types of change, shape and size. Change of shape is topology change - the Calabi-Yau becomes a different Calabi-Yau. Change of size means that topology remains the same, but the size of the extra dimensions (more precisely, the size of various benchmark curves and surfaces in the Calabi-Yau) changes.

    These size-parameters are called moduli in geometry, and in principle they can show up in 4d geometry as "moduli fields", one for each size-parameter of the Calabi-Yau. They are - if I have understood this stuff correctly - nothing but graviton modes within the Calabi-Yau, and they can interact with the other string modes. One of the challenges of string model-building is to "stabilize the moduli", i.e. to ensure that the size of the extra dimensions settles down and stays small, rather than blowing up into something unlike the real world. But even in a model where the moduli are stable, they can still matter e.g. in the very early universe, where they will be part of the give and take of energy in the big bang plasma.
  4. Apr 2, 2017 #3


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    In that case couldn't we call virtual gravitons to be virtual photons with some special property.
  5. Apr 4, 2017 #4
    A graviton has twice the spin of a photon, it's a different vibratory state of the string. Also, a graviton can interact with anything, whereas a photon can only be emitted or absorbed by a charged particle.

    In a string theory, that often means that a photon-string is stuck to a particular brane, and can only interact with strings that are also attached to that brane - to be attached to that brane is then what it means to be charged, and that's how the specificity of the photon's interactions is implemented - whereas a graviton-string moves freely through the space between branes, and can interact anywhere, thus the universality of gravity.
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