We analytically solve the conformal bootstrap equations in the regge limit for large n conformal field theories. These lectures notes are based on 8 3 hours of lectures given for graduate students. Fourpoint amplitude from open superstring field theory. The adscft correspondence states a duality between string theories living on antide sitter space and superconformal quantum field theories in minkowski space. Gardiner and jun hu winter, 2005, hri, allahabad, india. Abstract we present a brief exposition of teichmullers. The purpose of string theory is to describe the elementary particles and the fundamental interactions of nature, including gravitation as a quantum theory. The problem of strong coupling for sun gauge theories can be for.
The main subject of this thesis is scattering amplitudes in n4 superyangmills theory sym and n8 supergravity theory sugra. The basic theoretical framework particle physicists use to describe the. The corresponding story for the m5brane is the 6d superconformal gauge field theory. Introduction an orientation preserving homeomorphism f from a riemann surface x onto a riemann surface y is given. Lance dixon, paul ginsparg, and jeffrey harvey, c 1 \hat c 1 superconformal field theory. Probing n2 superconformal field theories with localization. Ironically, they discovered a beautiful theory that is not the desired dual of mtheory on ads4 s7. Pando zayas, chair professor dante amidei professor. This results can beapplied to construct a freefield theory on the volumeof the n 1superbrane. Campus, taramani madras 600 1 abstract in these lectures, we provide a introduction to conformal field theory with applications to condensed matter physics in mind. We consider sphere partition functions of ttdeformed large nconformal. Nevertheless there were a number of very useful field theories around for ex.
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. Topological phase of n 2 superconformal field theory and. New topological field theories from dimensional reduction of. Jonathan bagger, neil lambert, modeling multiple m2s, phys. Suresh govindarajan the institute of mathematical sciences c. Conformal eld theory has been an important tool in theoretical physics during the last decades. A theoryfield can fail to be linear on the basis that one cannot add solutions. Consequently, conformal eld theory is a very broad subject. Instanton effects in stringmtheory from 3d superconformal field theories masazumi honda indian strings meeting 2014 harishchandra research institute. Type iib superstring theory on ads5 s5 is dual to a scft in 4d n 4 sym theory.
The large n limit of superconformal field theories and supergravity juan maldacena1 lyman laboratory of physics harvard university cambridge, ma 028, u. In this thesis aspects of superconformal field theories that are of interest in the socalled adscft correspondence are investivated. Topics in holography and four dimensional superconformal. In theoretical physics, the sixdimensional 2, 0 superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. Nov 02, 2015 pdf we use supersymmetric localization to study probes of four dimensional lagrangian n2 superconformal field theories. We study in this thesis the superconformal index of 4dimensional n 2 supnq gauge eld theories on s1 s3. 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. Superconformal algebra in dimension greater than 2.
The original article on the n 8 n8case the blg model. Superconformal field theory in dimension d 2 d 2, locally given by a super vertex operator algebra for central charge 15 this is the worldsheet theory of the superstring may be regarded as a 2spectral triple see there for more, the 2dimensional generalization of spectral triples describing the quantum mechanics of spinning particles superparticles. On large n conformal theories, field theories in antide. In preparing these notes i referred to notes of tong ton and ginsparg gin89, as well as the book fs10 of frischman and sonnenschein. Volovich steklov mathematical institute, russian academy of sciences gubkin st.
Over the last several decades, our understanding of conformal eld theories has advanced signi cantly. We find that the renyi entanglement entropy of the. The largen limit of superconformal field theories and. 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. Introduction the purpose of the present paper is to address an old question posed by segal 37 to. We conjecture that compactifications of mstring theory on various antidesitter spacetimes are dual to various conformal field theories. Its role, if any, in string theorymtheory is still unclear. The author, following on from his previous work nashsen. Conformal group in ddimensions we begin here with an introductionto the conformalgroupinddimensions. New topological field theories from dimensional reduction.
A conformal field theory cft is a quantum field theory that is invariant under conformal. Volume 250, number 1,2 physics letters b 1 november 1990 topological phase of n 2 superconformal field theory and topological landauginzburg field theory kei ito lyman laboratory of physics, harvard university, cambridge, ma 028, usa received 4 june 1990 we construct a topological invariant version of twodimensional landauginzburg field theory which turns out to describe the topological. Despite the inherent difficulty in studying this theory, it is. A boundary condition is specified by two types of data. We then show that the nassociated superconformal symmetry is infinite dimensional and leads ton copies of supervirasoro algebra. Superconformal field theory and noncommutative geometry. We also give an interpretation of the large sspectrum in the spirit of the work of alday and maldacena 2. These constraints are much tighter than in two dimensions and must be satis ed by any conformal eld theory dual to einstein gravity. Mathematical aspects of sixdimensional quantum field theories december 8th12th, 2014. Mathematical aspects of sixdimensional quantum field theories. Browse other questions tagged quantum field theory liealgebra or ask your own question. A theory with these properties and so4 gauge symmetry was constructed by bagger and lambert and independently by gustavsson in 2007.
Scattering amplitudes and extra dimensions in adscft sissa. 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. Pdf probing n2 superconformal field theories with localization. Conformal bootstrap in the regge limit springerlink. 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. The application to string theory was explained by friedan, martinec and shenker in conformal invariance, supersymmetry and string theory, nucl. Next, we analyze strongly coupled largen cfts from both the fieldtheoretic and holographic viewpoints. On large n conformal theories, field theories in antide sitter. 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. This theory provides an important example of conformal field theory with higher. A theory field can fail to be linear on the basis that one cannot add solutions. S 5 has been studied 8, 9, 1 by analyzing critical points of n8 gauged supergravity.
Abstract we show that the large n limit of certain conformal field theories in various dimensions include in their hilbert space a sector describing. New n1 superconformal field theories and their supergravity. Holographic reconstruction of ads exchanges from crossing. Runkel2 1 california institute of technology, center for the physics of information, pasadena, ca 91125, usa email. Pdf we use supersymmetric localization to study probes of four dimensional lagrangian n2 superconformal field theories. Recently, gubser, klebanov and polyakov and witten have conjectured that the generating functional for certain correlation functions in conformal field theory is. The formalism of 2dsuperconformal field theory is also developed onsmc n n. Recently, deformations of the usual iib string theory on ads 5. Entanglement of local operators in largen conformal field theories. Symmetries of maldacenawilson loops from integrable string theory pdf version edoardo vescovi emmy noether group perturbative and nonperturbative approaches to string sigmamodels in. Unlike the case of real or complex valued fields, or in slightly more generality fields taking values in vector spaces, there is no natural way to define the sum.
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. Superconformal quantum field theories in stringgauge theory dualities pdf version andreas rodigast. On large nconformal theories, field theories in antide sitter space and singletons i. We study several aspects of the scattering amplitudes of these two theories using modern techniques. 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. Volume 250, number 1,2 physics letters b 1 november 1990 topological phase of n 2 superconformal field theory and topological landauginzburg field theory kei ito lyman laboratory of physics, harvard university, cambridge, ma 028, usa received 4 june 1990 we construct a topological invariant version of twodimensional landauginzburg field theory. Ahlfors used quasiconformal mappings in his geometric approach to nevanlinnas value distribution theory. Conformal field theory, boundary quantum field theory, wilson, t hooft and polyakov loops arxiv eprint.
The schur index of 4d n2 superconformal field theories. New topological field theories from dimensional reduction of nonlinear gauge theories noriaki ikeda ritsumeikan university, japan collaboration with k. It was proposed by maldacena that the large n limit of certain conformal field theories can be described in terms of. String theory has not yet reached the status to make falsi. 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. This question has recently become much more pressing due to the work of mike hopkins and. Its origins can be traced back on the one hand to statistical mechanics, and on the other hand to string theory.
Matthias r gaberdiel submitted on 19 oct 1999, last revised 1 nov 1999 this version, v2 abstract. Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. It is still poorly understood because there is no known description of the theory in terms of an action functional. This leads to a new proposal for a definition of mtheory which could be extended to include five noncompact dimensions.
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. 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. Perturbatively, this quantum field theory is the canonically quantized field theory. Symmetries of maldacenawilson loops from integrable string theory pdf version. The large n limit of superconformal field theories and. Conformal field theory and elliptic cohomology introduction. Abstract it was proposed by maldacena that the large n limit of certain conformal. These constraints are much tighter than in two dimensions. Localization and dualities in threedimensional superconformal field theories thesis by brian willett in partial ful llment of the requirements. Superconformal field theory and noncommutative geometry yasu kawahigashi university of tokyo nashville, may 5, 2012 yasu kawahigashi tokyo scft and ncg nashville, 552012 1 17. There will be minicourses given by david benzvi, university of texas, austin. Thesesprizes quantum field and string theory group. The a priori measure of the 2d model is a functional integral on the classical fields a quantum field theory in spacetime.
Quantum field theory beyond the standard model and string theory prof. We derive necessary and sufficient conditions for large n conformal field theories to have a universal free energy and an extended range of. Infinite conformal symmetry in twodimensional quantum field theory pdf. Conformal field theory 22 features of the theory do, and therefore the conformal structure is an integral part of the theory.
Historically the most important impetus came from statistical mechanics, where it described and classi ed critical phenomena. A comprehensive introduction to twodimensional conformal field theory is. Abstract we explore supersymmetric quantum field theories in three and four dimensions via an analysis of their bps spectrum. 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.