The adscft correspondence 1, 2 is one of the most important developments in the history of theoretical physics. The original conjecture of the adscft correspondence was made by. This has a description both in terms of open and closed strings. This is because the duality is becoming a powerful tool to analyze the real world. Some examples of this kind of duality are the klebanovstrassler duality 3 or the ns5braneslst 4. In a nutshell, this involves a duality that is, an exact physical equivalence between a quantum mechanical theory without gravity a yangmills theory. Starting with the conceptual basis of the holographic dualities, the subject is developed emphasizing some concrete topics, which are discussed in detail.
Although the adscft correspondence is often useful for studying the properties of black holes, most of the black holes considered in the context of adscft are physically unrealistic. A simple introduction to adscft and its application to. This subtlety is important for the conifold model, because it contains such. Using as a binding bridge superstring theory, or, more concretely, some theoretical aspects in the interaction between superstrings and dbranes, the maldacena conjecture establishes that. Such a map was given in 23, 24 and makes the correspondence much more explicit. The conjecture is tested by comparing the spin2 kaluzaklein modes and spin2 operators in the dual cft, and by comparing the gravitional euclidean action of the gravitational solution and free energy of the dual cft. In general, conformal field theory can make sense on a manifold of negative scalar curvature, but the specific conformal field theories that arise in the adscft correspondence, at least in the examples studied so far, are wellbehaved only when the scalar curvature of a is nonnegative. Then we use the adscft correspondence to compute the twopoint correlation functions on the boundary. In some sense, it is believed that the adscft correspondence as summarized by 14. I tried to include references to most relevant papers, but the emphasis was on papers. And so for this ads, by definition, the isometry would be sod,2, because this is hyperbole for ads, because the ads is defined as a hyperboloid in this d plus 2 dimensional minkowski spacetime with signature 2,d. The 10dimensional geometry is ads 5 s5 and its bound. A very introductory adscft yuxiao wu enrico fermi institute and department of physics, the university of chicago, chicago, il 60637, usa feb. This is a pedagogical introduction to the adscft correspondence.
Quantitatively, the adscft correspondence is a statement about the generating functional of a quantum eld theory and its dual theory of quantum gravity. Adscft stands for antide sitterconformal field theory, an expression thats not particularly elucidating. It is shown that the gauge dependence concentrates on. Supersymmetric wilson loops in the adscft correspondence. The conjecture conjecture the adscft correspondence 4dimensional n 4 su n sym and type iib sring theory on ads 5 s5 are two di erent descriptions of the same underlying physics, and we say that the two theories are dual to each other miguel angel martin contreras a brief introduction to adscft correspondence.
The adscft correspondence is intuitively a manifestation of the holographic principle conjectured by susskind and thooft, according to which in a quantum theory of gravity, the physical information in an a region of space is completely encoded i. This duality now goes under the name of adscft correspondence. Mit opencourseware lecture notes hong liu, fall 2014. Makoto natsuume adscft duality user guide september 1, 2016 springer arxiv. Since the fourdimensional theory is believed to be a conformal. Indeed, as explained above, most versions of the adscft correspondence involve higherdimensional models of spacetime with unphysical supersymmetry. Recently conformal eld theory appeared in yet another context, namely the \adscftcorrespondence, where also higher dimensional superconformal invariance is relevant. Adscft correspondence and integrability based on collaborations with n. Ads cft, a historical view on its stringy perspective.
Adscft from the perspective of effective field theory and the conformal bootstrap. Introduction to the adscft correspondence imperial college. Geometrical approximation to the adscft correspondence. This is the writeup of a series of lectures and is not aimed to. Since then the conjecture has been generalized to other backgrounds and gauge theories, so that nowadays we can more ads. Pdf adscft correspondence in condensed matter researchgate.
Just being able to nd a match is some con rmation of the adscft correspondence. Here r 1is the boundary of ads, and r 0 can be thought of as a horizon. Ads cft as a tool to study strongly coupled qfts and also discuss very brie. We postpone a more detailed phrasing of the correspondence till x3, after we have put it into historical context and explained the necessary ingredients in x2. The adscft correspondence is one of the largest areas of research in string theory.
Over the intervening years, the ads cft correspondence has owered into a vast and intri cate subject. The open stringdescriptionreduceston4superyangmillstheory,whereastheclosedstring. Adscft correspondence partition functions of cft and the string theory are related hexp r d4x. One physical system which has been studied using the adscft correspondence is the quarkgluon plasma, an exotic state of matter produced in particle accelerators. For example, it turns out that one prediction of ads cft is indeed close to the experimental results of the real quarkgluon plasma. How does adscft correspondence help in resolving the. The maldacena conjecture is that all the important dynamics at least in. And this hyperboloid preserves the lorentz transformation. This is usually done by comparing propagators on the string side with 2operator correlators hooion the cft side. Want to have an ads background to describe a strongly coupled. The complete knowledge of the generating functional allows us to know all that there is to know about a given theory. S5,whosemassisrelated tothescalingdimensionoftheoperatoraccordingto6. This extraordinary correspondence, later rephrased as gaugegravity duality, suggests that there exists a. The adscft correspondence is one of the most significant results that string.
The adscft correspondence 1 derives a fourdimensional conformal eld theory from type iib superstring theory by choosing as a vacuum vedimensional antide sitter space, whose symmetry so4,2 is the same as the fourdimensional conformal group. The adscft correspondence has, since it is proposed in 1997, ignited an animated research program and drawn attention from various theoretical and even experimental societies. Maldecenas original paper 1 alone now has well over 10,000 citations. This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies. S5 background to describe super yangmills, a conformal theory living in fourdimensional. Adscft as a tool to study strongly coupled qfts and also discuss very brie. In its strongest form, the adscft correspondence states that z qft z. This puts powerful constraints on cft correlation functions when we combine it with the fact that only. The adscft correspondence is at its heart the observation witten 98. Adscft is a particular, and deeply surprising, example of a duality. Pdf lovelock theory is the natural extension of general relativity to higher dimensions. Pdf the goal of these notes is to introduce, in a very elementary way, the idea of the anti desitterconformal field theory adscft correspondence. There is a third convenient coordinate system for ads. It involves only free strings on the string side, but generally interacting elds on the cft side.
Introduction to the adscft correspondence springerlink. To describe it, we rst consider the ads side, and in particular, we consider a. We shall also extend the correspondence to the nonconformal case and discuss the holographic description of con. Isbn 9781107085855 t he antide sitterconformal field theory adscft correspondence, also known as holographic duality, is a conjectured relation between quantum field theory and a higherdimensional gravity theory. Next, one takes a suitable lowenergy limit ofthe system, which involves taking ls 0. Adscft correspondence subir sachdev department of physics, harvard university, cambridge, massachusetts, 028, usa and perimeter institute for theoretical physics, waterloo, ontario n2l 2y5, canada dated.
One answer is provided by the adscft correspondence or, more accurately, conjecture, since it remains to be conclusively proven, discovered within the general framework of string theory. The large n limit of superconformal field theories and supergravity, adv. In all the three cases mentioned above, the bulk is a noncompact manifold endowed with gravity, such that the dual. These issues are still very much at research level and my discussions will mainly be introductory.
Adscft correspondence 2 is the most relevant realization of the gravitygauge duality, but is not the only successful one. Adscft correspondence with applications to condensed. Sorry, but im damned if i know if it even does help resolve the black hole information paradox, or if there even is a black hole information paradox. Section 2 of this paper is devoted to some details of the ads cft correspondence that will arise in our analysis. Zaffaroni, introduction to the adscft correspondence. Adscft correspondence, the subject of this dissertation. Quantumaspectsofgaugetheories,supersymmetryanduni cation proceedings introduction to the adscft correspondence igor r. String theory on ads 5 5s the adscft correspondence scaling functions of the adscft the bes scaling function and its generalization comparison with string theory twist operators and the bfkl equation the ysystem conjecture conclusions adam rej imperial college london 09. Adscft, a historical view on its stringy perspective. Finally, we briefly discuss examples of cftads correspondence with less supersymmetry and the holographic renormalization group. On ads3cft2 for d1d5 brane bound states and black hole entropy in string theory juan maldacena, section 4 of. Need a black hole in that background with surface gravity. Then i describe the basic adscft scenario, of n 4 super yangmillss relation to string theory in ads 5.
Introduction to the adscft correspondence 1 introduction. To derive the adscft correspondence, one starts with a stack of d3branes. The adscft correspondence in the form in which it was proposed in 1 did not yet provide a detailed map between ads and cft quantities. A simple introduction to adscft and its application to condensed. Ads 5 5s, and the maximally supersymmetric yangmills theory. Adscft duality and the emergence of spacetime sciencedirect. Speci cally, the adscft correspondence is the conjectured duality between a quantum string theory living on a particular 10dimensional geometry and a speci c quantum eld theory qft living on the boundary of that geometry.
467 155 1366 1327 493 643 1124 1428 864 1393 1271 1022 1487 116 1198 1209 972 362 1025 741 951 369 1043 502 944 910 1119 777 33 386 581 335 1246 148 265 453 1183 857