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code 128 generator vb.net Now since R = ( gs N )1/ 4 we can write N dof = in Java
Now since R = ( gs N )1/ 4 we can write N dof = Scan QRCode In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Painting QRCode In Java Using Barcode maker for Java Control to generate, create QR Code ISO/IEC18004 image in Java applications. String Theory Demysti ed
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Now if we take S = A/4G then we nd
3 TSYM =
A R3
Now we regulate the SYM so that the maximum TSYM is 1/d. Then we nd the maximum area to be Amax = R3 3 Regulation of the super YangMills theory on the boundary gives a holographic description with one bit per Planck area. An interesting result derived by Susskind and Witten is the IRUV connection. This relates IR divergences in the bulk to UV divergences on the boundary. Consider a string in the bulk that ends on the boundary. The ends of the string correspond to a point charge in the YangMills theory. Now, just thinking back to the selfenergy of an electron, you will realize that a point charge in the YangMills theory has a divergent in nite selfenergy. This is an UV divergence. The divergence of the bulk string is proportional to 1/d, while d plays the role of a short distance regulator for UV divergence in SYM theory. The energy of the string is linearly divergent at the boundaries. Since this divergence is softer, we say that it is an IR divergence. The propagator for a particle of mass m in the bulk is given by = X1 X 2
where we have relgulated the area using A R3 and 1. Super YangMills theory is a conformal eld theory. Remember Chap. 5 We learned how to calculate operator product expansions there. For super YangMills theory: Y ( X1 )Y ( X 2 ) = p X1 X 2 You can see that you can transform between these two expressions. What this means is that a propagator for a particle of mass m in the bulk can be transformed into a power law in the conformal eld theory on the boundary. String Theory Demysti ed
Summary In this chapter we provided a brief and heuristic introduction to two interesting ideas that have sprung from string theory: the holographic principle and the AdS/ CFT correspondence. These two ideas are related. The holographic principle tells us that for an enclosed volume, the informational content of the volume can be described by an equivalent theory that lives on the bounding surface area. This notion is codi ed in black hole mechanics where the entropy of the black hole is proportional to the area of the horizon, not the volume it encloses. The AdS/CFT correspondence describes a vedimensional universe where vedimensional supergravity in the bulk is equivalent to a super YangMills conformal eld theory on the boundary. Quiz
A solution of supergravity gives the metric for a Dbrane as: ds 2 = F ( z )(dt 2 dx 2 ) F ( z ) 1 dz 2 ags N where F ( z ) = 1 + 4 z 1/ 2 ags N z4
1. Find an expression for F(z) in the limit
2. Using your answer to Prob. 1, nd a new expression for the metric. 3. The holographic principle can be best described by (a) The informational content of a region is encoded in its volume. (b) The informational content of a region can be described entirely by the surface area. (c) Fields living in the bulk are not equivalent to elds living on the bounding surface. 4. In AdS/CFT correspondence, the number of degrees of freedom available to the super YangMills theory on the boundary is (a) Independent of the AdS geometry. (b) Related to the string coupling strength only. (c) Is related to the string coupling strength and the fundamental string length. (d) Is related to the fundamental string length only.

