By Aharony, Gubser, Maldacena, Ooguri, Oz.
We assessment the holographic correspondence among box theories and string/M conception, targeting the relation among compactifications of string/M idea on Anti-de Sitter areas and conformal box theories. We assessment the historical past for this correspondence and speak about its motivations and the facts for its correctness. We describe the most effects which were derived from the correspondence within the regime that the sector thought is approximated by means of classical or semiclassical gravity. We specialize in the case of the supersymmetric gauge idea in 4 dimensions, yet we talk about additionally box theories in different dimensions, conformal and non-conformal, without or with supersymmetry, and specifically the relation to QCD. We additionally speak about a few implications for black gap physics.
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Extra resources for Large N field theories, string theory and gravity
Sample text
Green functions of free "elds on AdS N> have been computed in [97,98] using this method. The Euclidean AdS can be mapped into a (p#2)-dimensional disk. In the coordinates N> (u, t , x), u"R is the sphere SN> at the boundary with one point removed. The full boundary # sphere is recovered by adding a point corresponding to u"0 (or equivalently x"R). This is shown in Fig. 8 in the case of AdS , for which z"t #i/u gives a complex coordinate on the # upper-half plane. By adding a point at in"nity, the upper-half plane is compacti"ed into a disk.
Su$cient, to have large N in order to have a weakly coupled supergravity description. One might wonder why the above argument was not a proof rather than a conjecture. It is not a proof because we did not treat the string theory non-perturbatively (not even nonperturbatively in ). erent forms of the conjecture. In its weakest form the gravity description would be valid for large g N, but the full string theory on AdS might not agree with the "eld theory. A not so weak form would say that the conjecture is valid even for "nite g N, but only in the NPR limit (so that the corrections would agree with the "eld theory, but the g corrections may not).
34) O. Aharony et al. / Physics Reports 323 (2000) 183}386 219 with a"(l# ! R) , ! b"(l# # R) , ! 35) and "(p#1)$((p#1)#4(mR) . 37) IJ I J IJ IJ I J IJ is conserved for any constant value of . 32). The choice of for each scalar "eld depends on the theory we are considering. 38) is conserved only if the energy-momentum #ux through the boundary at " /2 vanishes, d (gn ¹G "0 . 2 )R #2 tan ] P0 ( P /2) . 34) is an integer. If we require the energy to be real, we "nd " "R" #l#2n (n"0, 1, 2,2) .