Adscft, a historical view on its stringy perspective. Maldecenas original paper 1 alone now has well over 10,000 citations. These issues are still very much at research level and my discussions will mainly be introductory. 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. Starting with the conceptual basis of the holographic dualities, the subject is developed emphasizing some concrete topics, which are discussed in detail. Ads cft, a historical view on its stringy perspective. One physical system which has been studied using the adscft correspondence is the quarkgluon plasma, an exotic state of matter produced in particle accelerators.
Supersymmetric wilson loops in the adscft correspondence. The adscft correspondence is one of the largest areas of research in string theory. Some examples of this kind of duality are the klebanovstrassler duality 3 or the ns5braneslst 4. This is the writeup of a series of lectures and is not aimed to. Want to have an ads background to describe a strongly coupled. In some sense, it is believed that the adscft correspondence as summarized by 14. 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. Indeed, as explained above, most versions of the adscft correspondence involve higherdimensional models of spacetime with unphysical supersymmetry.
This duality now goes under the name of adscft correspondence. Since then the conjecture has been generalized to other backgrounds and gauge theories, so that nowadays we can more ads. The adscft correspondence is one of the most significant results that string. Makoto natsuume adscft duality user guide september 1, 2016 springer arxiv. Quantitatively, the adscft correspondence is a statement about the generating functional of a quantum eld theory and its dual theory of quantum gravity. 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. The open stringdescriptionreduceston4superyangmillstheory,whereastheclosedstring. Then we use the adscft correspondence to compute the twopoint correlation functions on the boundary. Section 2 of this paper is devoted to some details of the ads cft correspondence that will arise in our analysis. Introduction to the adscft correspondence 1 introduction. 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. The 10dimensional geometry is ads 5 s5 and its bound.
Here r 1is the boundary of ads, and r 0 can be thought of as a horizon. To derive the adscft correspondence, one starts with a stack of d3branes. Pdf adscft correspondence in condensed matter researchgate. Mit opencourseware lecture notes hong liu, fall 2014. The maldacena conjecture is that all the important dynamics at least in. This extraordinary correspondence, later rephrased as gaugegravity duality, suggests that there exists a. Just being able to nd a match is some con rmation of the adscft correspondence.
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. S5 background to describe super yangmills, a conformal theory living in fourdimensional. How does adscft correspondence help in resolving the. Geometrical approximation to the adscft correspondence. We shall also extend the correspondence to the nonconformal case and discuss the holographic description of con. There is a third convenient coordinate system for ads. Over the intervening years, the ads cft correspondence has owered into a vast and intri cate subject. Pdf lovelock theory is the natural extension of general relativity to higher dimensions. This is usually done by comparing propagators on the string side with 2operator correlators hooion the cft side. Adscft stands for antide sitterconformal field theory, an expression thats not particularly elucidating. 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. 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. The adscft correspondence 1, 2 is one of the most important developments in the history of theoretical physics. Next, one takes a suitable lowenergy limit ofthe system, which involves taking ls 0.
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. Since the fourdimensional theory is believed to be a conformal. It involves only free strings on the string side, but generally interacting elds on the cft side. Adscft correspondence partition functions of cft and the string theory are related hexp r d4x. Adscft is a particular, and deeply surprising, example of a duality. This puts powerful constraints on cft correlation functions when we combine it with the fact that only.
To describe it, we rst consider the ads side, and in particular, we consider a. For example, it turns out that one prediction of ads cft is indeed close to the experimental results of the real quarkgluon plasma. Finally, we briefly discuss examples of cftads correspondence with less supersymmetry and the holographic renormalization group. 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. In all the three cases mentioned above, the bulk is a noncompact manifold endowed with gravity, such that the dual. And this hyperboloid preserves the lorentz transformation. Pdf the goal of these notes is to introduce, in a very elementary way, the idea of the anti desitterconformal field theory adscft correspondence. It is shown that the gauge dependence concentrates on. Adscft correspondence and integrability based on collaborations with n. 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. Then i describe the basic adscft scenario, of n 4 super yangmillss relation to string theory in ads 5. Recently conformal eld theory appeared in yet another context, namely the \adscftcorrespondence, where also higher dimensional superconformal invariance is relevant.
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. Adscft duality and the emergence of spacetime sciencedirect. This has a description both in terms of open and closed strings. A very introductory adscft yuxiao wu enrico fermi institute and department of physics, the university of chicago, chicago, il 60637, usa feb. Quantumaspectsofgaugetheories,supersymmetryanduni cation proceedings introduction to the adscft correspondence igor r. The adscft correspondence is at its heart the observation witten 98. The complete knowledge of the generating functional allows us to know all that there is to know about a given theory. 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.
The large n limit of superconformal field theories and supergravity, adv. Zaffaroni, introduction to the adscft correspondence. In a nutshell, this involves a duality that is, an exact physical equivalence between a quantum mechanical theory without gravity a yangmills theory. 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. Introduction to the adscft correspondence imperial college. This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies. Such a map was given in 23, 24 and makes the correspondence much more explicit. Adscft correspondence 2 is the most relevant realization of the gravitygauge duality, but is not the only successful one. Ads cft as a tool to study strongly coupled qfts and also discuss very brie. Adscft correspondence, the subject of this dissertation. 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 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. It relates two very different theories and at first sight seems obviously wrong. I tried to include references to most relevant papers, but the emphasis was on papers. Adscft from the perspective of effective field theory and the conformal bootstrap. S5,whosemassisrelated tothescalingdimensionoftheoperatoraccordingto6. This is a pedagogical introduction to the adscft correspondence. Adscft correspondence with applications to condensed. A simple introduction to adscft and its application to condensed. In its strongest form, the adscft correspondence states that z qft z.
This subtlety is important for the conifold model, because it contains such. Ads 5 5s, and the maximally supersymmetric yangmills theory. Need a black hole in that background with surface gravity. 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. Introduction to the adscft correspondence springerlink. This is because the duality is becoming a powerful tool to analyze the real world.