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Regulation of the super Yang-Mills theory on the boundary gives a holographic description with one bit per Planck area. An interesting result derived by Susskind and Witten is the IR-UV 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 Yang-Mills theory. Now, just thinking back to the self-energy of an electron, you will realize that a point charge in the Yang-Mills theory has a divergent in nite self-energy. 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 =

2

where we have relgulated the area using A R3 and 1. Super Yang-Mills theory is a conformal eld theory. Remember Chap. 5 We learned how to calculate operator product expansions there. For super Yang-Mills theory: Y ( X1 )Y ( X 2 ) = p X1 X 2

You had an xcdatamodel file, and now it has become an xcdatamodeld directory, with two xcdatamodel files in it If you click the disclosure triangle next to the Locationsxcdatamodeld, you will see that one of the files is current and one is not You can see that the file that is current is marked with a green check mark (see Figure 6-4)..

So our number, 6,783, would be written as follows in base two:

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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.

The first thing I always do when Xcode creates files with names like this is give the files better names I renamed the Locationsxcdatamodel file to Locations01xcdatamodel and renamed Locations 2xcdatamodel to Locations02xcdatamodel You know, over the years, if you count up all the bugs in Xcode that were triggered by a space in a path or a resource name, there are just too many to count Really, life is too short to take risks like that After you rename these files, take a moment to build and run the application It should run without an error But remember, you still have not made any changes to the schema Before you do make any changes, select the Locations02xcdatamodel file in Xcode, and select Design Data Model Set Current Version.

From right to left that s one 1, one 2, one 4, one 8, one 16, one 32, one 64, no 128s, no 256s, one 512, no 1,024s, one 1,048s, and one 4,096. Add them all up (1 2 4 8 16 32 64 512 2,048 4,096) and you should get 6,783. That s binary arithmetic. Most PCs today use the seven-bit ASCII character set shown in Table 2-1. The mainframe, however (remember the mainframe ), uses an eight-bit code called EBCDIC. What happens when a seven-bit ASCII PC sends information to an EBCDIC mainframe system that only understands eight-bit characters Clearly, problems would result. Something, therefore, has to take on the responsibility of translating between the two systems so that they can intelligibly transfer data between each other.

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The green check mark moves to the second file, and now you can make changes to this second file For example, you can add a whatever attribute of type String, and then you would see the whatever attribute in the application and could even assign a value to it Well, I m sure glad that s over! Actually, let s not get too excited Make sure you do not run your application yet, because you are not finished making changes You might want to take this opportunity to see what kinds of changes you can make to your schema and what kinds of things will cause problems While you are developing your application and running it to debug something and then making changes and running it again, there are definitely ways to cause yourself a problem.

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 ve-dimensional universe where ve-dimensional supergravity in the bulk is equivalent to a super Yang-Mills conformal eld theory on the boundary.

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