Hagedorn transitions in 10 D and 11 D string/M-theories?
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PROF. E. FRADKIN, MOSCOW, RUSSIA, JUNE 5-10. ... Hagedorn temperature for a ( six-dimensional supersymmetric) string theory ..... +(d˜xp+1)2 + ··· + (d˜x5)2 + H(f−1d˜r2 ..
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The number of dimensions varies (10, 11, 26) with the specific sub-group of string theory or M-theory you are referring to, but they all have the same three types of dimensions.
Three spatial dimensions. Known in common English as "depth", "width", "height". Or some similar grouping of three perpendicular angles that describe these spatial dimensions.
One temporal dimension. Known is common English as "time". Interestingly, while equations for entropy and energy exchange are unidirectional, the actual flow of time only proceeds in one direction. A phenomena known as the "arrow of time".
We call the grouping of these first four dimensions "spacetime".
The third type of dimension are those which are undergoing Compactification. The "size" of the dimensions is not apparent to us at the macro scale. These additional six or seven dimensions would be "curling" spatial dimensions that are bound to the three big spatial dimensions.
The analogy used to help laymen wrap their head around the math is to consider a big dimension to be like a garden hose. At many scales of looking at that hose, you fail to see it as anything but a line going in one dimension. But up close it has a perpendicular circumference that is curling around the central line of the dimension, this is the compactified small dimension.
(And then there is another type of compactification called T-duality which describes these extra dimensions in another way. One I don't grasp since I haven't studied this area of string theory.)
Three spatial dimensions. Known in common English as "depth", "width", "height". Or some similar grouping of three perpendicular angles that describe these spatial dimensions.
One temporal dimension. Known is common English as "time". Interestingly, while equations for entropy and energy exchange are unidirectional, the actual flow of time only proceeds in one direction. A phenomena known as the "arrow of time".
We call the grouping of these first four dimensions "spacetime".
The third type of dimension are those which are undergoing Compactification. The "size" of the dimensions is not apparent to us at the macro scale. These additional six or seven dimensions would be "curling" spatial dimensions that are bound to the three big spatial dimensions.
The analogy used to help laymen wrap their head around the math is to consider a big dimension to be like a garden hose. At many scales of looking at that hose, you fail to see it as anything but a line going in one dimension. But up close it has a perpendicular circumference that is curling around the central line of the dimension, this is the compactified small dimension.
(And then there is another type of compactification called T-duality which describes these extra dimensions in another way. One I don't grasp since I haven't studied this area of string theory.)
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