The large n limit of superconformal field theories and. There will be minicourses given by david benzvi, university of texas, austin. We give a short account of the recently constructed n2 d6 matter coupled supergravity based on the f4 exceptional supergroup and of its 5d superconformal theory correspondent. Nov 02, 2015 a read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and higgs branches are understood in terms of the general structure of relevant deformations of nontrivial n2 conformal field theories. New examples of n2 supersymmetric conformal field theories are found as fixed points of su2 n2 supersymmetric qcd. The basis consists of the obligatory courses on quantum and statistical field theory. We conjecture that compactifications of mstring theory on various antidesitter spacetimes are dual to various conformal field theories.
Ironically, they discovered a beautiful theory that is not the desired dual of mtheory on ads4 s7. The problem of strong coupling for sun gauge theories can be for. New n1 superconformal field theories and their supergravity. Simple superconformal field theories in two dimensions. This is shown bytaking some branes in the full mstring theory and thentaking a lowenergy limit where the field theory on thebrane. We show that the largen limits of certainconformal field theories in various dimensions includein their hilbert space a sector describing supergravityon the product of antide sitter spacetimes, spheres, and other compact manifolds. Pando zayas, chair professor dante amidei professor. In this thesis aspects of superconformal field theories that are of interest in the socalled adscft correspondence are investivated. In d the degeneration limits correspond to the di erent duality frames of su2 sym with nf 4 theory plus a decoupled hypermultiplet. In this paper we develop the superspacestructure of the multicomplex space mc n forn 2 n. Inverse bootstrapping conformal field theories springerlink. In theoretical physics, the sixdimensional 2,0 superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. Su3 theory, the third limit when two like punctures collide corresponds to the argyresseiberg theory.
Fourpoint functions in n2 superconformal field theories. Nahm university of bonn physics institute nussallee 12, d53115 bonn, germany abstract since 70 years, quantum eld theory has been one of the most important research areas of physics. These lectures notes are based on courses given at national taiwan university, national chiaotung university, and national tsing hua university in the spring term of 2015. The corresponding story for the m5brane is the 6d superconformal gauge field theory. We take the limit where the field theory on the brane decouples from the bulk. Fourpoint amplitude from open superstring field theory. Conformal field theory and elliptic cohomology introduction. We study several aspects of the scattering amplitudes of these two theories using modern techniques. Topics in holography and four dimensional superconformal field theories by ibrahima bah a dissertation submitted in partial ful llment of the requirements for the degree of doctor of philosophy physics in the university of michigan 2012 doctoral committee. Abstract we explore supersymmetric quantum field theories in three and four dimensions via an analysis of their bps spectrum.
A 6d superconformal field theory christian s amann and lennart schmidt maxwell institute for mathematical sciences department of mathematics, heriotwatt university colin maclaurin building, riccarton, edinburgh eh14 4as, u. Its role, if any, in string theorymtheory is still unclear. Superconformal quantum field theories in stringgauge theory dualities pdf version andreas rodigast renormalisation in perturbative quantum gravity pdf version. Recently, deformations of the usual iib string theory on ads 5. Quantum field theory qft is, in most general terms, the study of renormalization group rg ows, i.
These are followed by optional courses on subjects such as standard model, string theory, general relativity, cosmology, interacting electron systems, modelling and simulations and the manybody aspects of soft condensed matter. Superconformal algebra in dimension greater than 2. Pdf probing n2 superconformal field theories with localization. Perturbatively, this quantum field theory is the canonically quantized field theory. Its origins can be traced back on the one hand to statistical mechanics, and on the other hand to string theory. Maldacenas duality between conformal field theories and supergravity is applied to some conformal invariant models with eight supercharges. The original article on the n 8 n8case the blg model. We focus on conformal invariant field theories but a similar analysis could be done for nonconformal field theories. In four dimensions, we develop the theory of bps quivers which provides a simple picture of bps states in terms of a set of building block atomic particles, and basic quantum mechanical interactions. Tokyo n 2 scft and ncg bucuresti april 25, 2011 1 17 page 2.
Quallsa adepartment of physics, national taiwan university, taipei, taiwan email. A theory with these properties and so4 gauge symmetry was constructed by bagger and lambert and independently by gustavsson in 2007. We observe that, in this limit, we can still trust the near horizon geometry for large n. Fqft and cohomology 1,1dimensional euclidean field theories and k theory 2,1dimensional euclidean field theory. The author, following on from his previous work nashsen. Unitarity bounds and rg flows in time dependent quantum field theory. Thanks to the important progress during the past several years, there now also exists a large set of precisely formulated ads 4cft 3 conjectures. The main subject of this thesis is scattering amplitudes in n4 superyangmills theory sym and n8 supergravity theory sugra. The a priori measure of the 2d model is a functional integral on the classical fields a quantum field theory in spacetime. This is shown by taking some branes in the full mstring theory and then taking a low energy limit where the field theory on the brane. Differential topology for physicists, academic press, 1983, covers ellipitc differential and pseudodifferential operators, atiyahsinger index theory, morse theory, instanntons and monopoles, topological quantum field theory, string theory and knot theory.
Its role, if any, in string theory m theory is still unclear. An archive of recordings of the lectures at the 2014 berkeley workshop on mathematical aspects of the 2,0 superconformal field theory, organised by harri. Full text of new superconformal field theories in four. N 2 superconformal field theory and noncommutative geometry yasu kawahigashi university of tokyo bucuresti april 25, 2011 yasu kawahigashi univ. Large n superconformal gauge theories and supergravity. Let us consider the theory at the superconformal point, where r 0. Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for a. Probing n2 superconformal field theories with localization article pdf available in journal of high energy physics 20161 november 2015 with. F4 supergravity and 5d superconformal field theories. We extend the basic properties of themulticomplex analysis to n the case ofsmc n n, called supermulticomplex spaces. Symmetries in conformal field theory chris elliott these are elementary notes on virasoro and a ne lie algebra symmetries in 2d conformal eld theory, prepared for a seminar talk at northwestern.
Ironically, they discovered a beautiful theory that is not the desired dual of m theory on ads4 s7. We propose a novel approach to study conformal field theories. The adscft correspondence states a duality between string theories living on antide sitter space and superconformal quantum field theories in minkowski space. Topics in holography and four dimensional superconformal. This is shown bytaking some branes in the full mstring theory and thentaking a lowenergy limit where the field theory on thebrane decouples from the bulk. Jonathan bagger, neil lambert, modeling multiple m2s, phys. Maldacenas duality between conformal field theories and supergravity is applied to some conformal invariant models with 8.
This results can beapplied to construct a freefield theory on the volumeof the n 1superbrane. Exploring the space of superconformal field theories. Spalinski, large n superconformal gauge theories and. In theoretical physics, the sixdimensional 2,0superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. We show that the large n limit of certain conformal field theories in various dimensions include in their hilbert space a sector describing supergravity on the product of antidesitter spacetimes, spheres and other compact manifolds. This question has recently become much more pressing due to the work of mike hopkins and. The largen limit of superconformal field theories and. Historically the most important impetus came from statistical mechanics, where it described and classi ed critical phenomena. We show that the large limit of certain conformal field theories in various dimensions include in their hilbert space a sector describing supergravity on the product of antidesitter spacetimes, spheres and other compact manifolds. This leads to a new proposal for a definition of mtheory which could be extended to include five noncompact dimensions. The workshop is principally aimed at graduate students and young researchers working in the mathematics of quantum field theory and areas of mathematics to which it applies, such as geometric representation theory, geometric topology and mirror symmetry. Introduction the purpose of the present paper is to address an old question posed by segal 37 to. For further progress, it must become a standard domain of mathematical research, too. The schur index of 4d n2 superconformal field theories.
This check works very nicely for the correspondence between the coset space t 1,1 and the superconformal field theory from d3 branes at the conifold singularity. This leads to a new proposal for a definition of m theory which could be extended to include five noncompact dimensions. Superconformal field theory and noncommutative geometry. Aspects of superconformal field theories by abhijit gadde doctor of philosophy in physics stony brook university 2011 recently, a lot of progress has been made towards understanding the strongly coupled supersymmetric quantum gauge theories. Fqft and cohomology 1,1dimensional euclidean field theories and ktheory 2,1dimensional euclidean field theory. In conformal field theory, operator dimensions are bounded in a way. The large n limit of superconformal field theories.
Like the ordinary bcsystems, the super bcsystems are free theories described by quadratic lagrangians with firstorder derivatives. This is shown by taking some branes in the full mstring theory and then taking a low energy limit where the field. Pdf n 2 superconformal field theory and noncommutative. It is still poorly understood because there is no known description of the theory in terms of an action functional. Safdi3 1school of natural sciences, institute for advanced study, princeton, nj 08540 2center for the fundamental laws of nature, harvard university, cambridge, ma 028 3joseph henry laboratories, princeton university, princeton. Conformal eld theory has been an important tool in theoretical physics during the last decades. The cases considered include n parallel d3 branes in iib string theory and various others.
The formalism of 2dsuperconformal field theory is also developed onsmc n n. In general a superconformal field theory is a theory which is invariant under any weyl scalings and local supersymmetry transformations of the background metric and the gravitino field. Finally, we discuss a simple method to obtain correlators in general \cal n2 superconformal field theories in perturbation theory in terms of. In preparing these notes i referred to notes of tong ton and ginsparg gin89, as well as the book fs10 of frischman and sonnenschein. Given kacs classification of finitedimensional simple lie. We then show that the nassociated superconformal symmetry is infinite dimensional and leads ton copies of supervirasoro algebra. Apr 10, 2008 this is shown by taking some branes in the full mstring theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We study in this thesis the superconformal index of 4dimensional n 2 supnq gauge eld theories on s1 s3. Mathematical aspects of sixdimensional quantum field. S 5 has been studied 8, 9, 1 by analyzing critical points of n8 gauged supergravity. Request pdf fourpoint functions in n2 superconformal field theories fourpoint correlation functions of hypermultiplet bilinear composites are analysed in n2 superconformal field theory.
1229 497 407 989 715 502 639 1423 902 468 490 1139 1007 514 312 935 278 254 834 469 242 617 382 1477 1267 1315 870 1519 1119 296 82 1262 176 1012 739 1486 758 491 1314 670 783 848 17 162 1313 1019