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. As the conformal supergravity is a higherderivative theory, to analyze the secondorder. Mario martone is a postdoctoral scholar in particle physics at the university of texas at austin. In the previous paper 2 we have considered the quantum superkdv 3, 4, 5 hierarchy, which give rise to the infinite number of commuting integrals of motion im, constructed via the generators of the superconformal algebra and therefore leading to. Boundary states, onepoint structure constants, and bootstrap equations for the boundarybulk structure constants are derived. Petersburg, russia b department of high energy physics, physics faculty, st. He did his undergraduate studies there before moving to syracuse university, ny, usa where he got his first phd degree in noncommutative geometry. To leading order, the change in the action is given by 6s 6gi s cpzviz, z. 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. Superconformal field theory in dimension d2, locally given by a super vertex operator algebra. Tokyo n 2 scft and ncg bucuresti april 25, 2011 1 17 page 2. This technique allows for the calculation of the exact dimension of chiral operators for superconformal field theories scfts and, in some cases, it unravels some of the dynamics of chiral gauge theories. Boundary states, onepoint structure constants, and bootstrap equations for.
Fermionic model of superconformal field theory with boundary is considered. Introduction to superconformal field theory proceedings of. Researchers at stanford and boston university construct two dimensional cfts with the right properties to be holographic duals of threedimensional supergravity. Mavromatos department of physics theoretical physics kings college london strand, london wc2r 2ls, u. In our last paper 4, however, we argued that this theory has a classical. Topological twist in n2 superconformal field theory, i. The neveuschwarz and ramond algebras of logarithmic superconformal field theory n. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and moonshine, connections to subfactor theory and noncommutative geometry. For this model, the bootstrap equations for boundary structure constants are derived. In, a criterion was similarly proposed for 2, 2 superconformal theories dual to pure extended supergravity in ads 3. In this thesis, we discuss 3d3d correspondence between chernsimons theory and threedimensional n 2 superconformal field theory. 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.
Introduction to superconformal field theory proceedings. The large n limit of superconformal field theories and. N2 superconformal field theories in fourdimensions and a. Aspects of superconformal field theories graduate program in. This thesis describes the structures of sixdimensional 6d superconformal field theories and its torus compactifications.
An archive of recordings of the lectures at the 2014 berkeley workshop on mathematical aspects of the 2,0 superconformal field theory, organised by harrison chen, chris elliott, david nadler. We conjecture that compactifications of mstring theory on various antidesitter spacetimes are dual to various conformal field theories. N 2 superconformal field theory and noncommutative geometry yasu kawahigashi university of tokyo bucuresti april 25, 2011 yasu kawahigashi univ. The recent interplay between antidesitter supergravity and conformal field theories follows from the conjectured duality 5 between the string or mtheory. Juan maldacena, the large n limit of superconformal field theories and supergravity, adv. We consider superconformal field theories with central charge c. It is a widely held belief that for more than one m5brane, this theory is nonlagrangian and exists only at quantum level. The hamiltonian formalism for the n1, d4 superconformal system is given. An extremal n2 superconformal field theory by phil brown on november 14, 2017. In the 3d3d correspondence proposed by dimoftegaiottogukov information of abelian flat connection in chernsimons theory was not captured. New examples of n2 supersymmetric conformal field theories are found as fixed points of su2 n2 supersymmetric qcd. Derivation of the abelian 6d theory to low order as the small fluctuations of the greenschwarz sigmamodel of the m5brane around a solution embedding as the asymptotic boundary of the adsspacetime nearhorizon.
Superconformal field theory and susy n1 kdv hierarchy i. Logarithmic primary fields in conformal and superconformal. Mirror symmetry and moduli spaces of superconformal field theories. Studies of superconformal field theories using glsm and. Also, the dual scfts in 3d and 6d are much more elusive. Aspects of conformal and superconformal field theory arxiv. Historically the most important impetus came from statistical mechanics, where it described and classi ed critical phenomena. Szabo department of mathematics heriotwatt university riccarton, edinburgh eh14 4as, u. The hamiltonian formalism for then1,d4 superconformal system is given.
Then a lagrangian description of the 3d theory was constructed the abjm theory. Recently, a lot of progress has been made towards understanding the strongly coupled supersymmetric quantum gauge theories. The problem of strong coupling for sun gauge theories can be for. In the same way as conformal symmetry was a remnant of the reparametrization invariance of the bosonic string in conformal gauge, superconformal invariance is a remnant of local supersymmetry of the fermionic string in super conformal gauge. Integrable structure of superconformal field theory and. Superconformal field theory and noncommutative geometry. Superconformal field theory on threebranes at a calabiyau. Conformal eld theory has been an important tool in theoretical physics during the last decades. Links between certain stochastic evolutions of conformal maps and conformal field theory have been studied in the realm of sle and by utilizing singular. Using these blocks, we study crossing symmetry constraints both numerically and analytically.
We find five continuous oneparameter families of theories all interconnected. Mirror symmetryis the remarkable discovery in string theory that certain mirror pairs of calabiyau manifolds apparently produce isomorphic physical theories. And this is the way that in the abelian case and for just the 2form sector witten has studied the 6d theory since. The supersymmetry invariant integrable structure of twodimensional superconformal field theory is considered. This procedure can also be applied to superconformal theories, although in general the perturbation will break supersymmetry, leaving only a conformal field. On stochastic evolutions and superconformal field theory. This is shown by taking some branes in the full mstring theory and then taking a low energy limit where the field. We conjecture that compactifications of mstring theory on various anti desitter spacetimes is dual to various conformal field theories. Mtheory is less well understood than type iib superstring theory.
N2 superconformal field theory and operator algebras. A theory with these properties and so4 gauge symmetry was constructed by bagger and lambert and independently by gustavsson in 2007. In my talk i will explain the motivations behind the study of quantum field theories in 4 dimensions which have both supersymmetry and conformal invariance and will give a flavor of the wonderful mathematics involved in these studies. Edward witten, section 1 of some comments on string dynamics hepth9507121.
It is still poorly understood because there is no known description of the theory in terms of an action functional. A notion of reflection is introduced which, in special circumstances, produces a. Riemann surface can be decomposed into pairs of pants in a variety of ways. Its origins can be traced back on the one hand to statistical mechanics, and on the other hand to string theory. The classical limit of the corresponding infinite family of integrals of motion im coincide with the family of im of susy n 1 kdv hierarchy. Let us consider the theory at the superconformal point, where r 0.
The action of s duality on the gauge parameter space is the same as the action of the mapping class group of the riemann surface on its complex moduli space. It is known that the superconformal field theory possesses two integrable structures. For a long time it was believed that these 3d and 6d theories do not have a lagrangian description. The superconformal blocks for the fourpoint function are computed by analyzing superconformal ward identity. Threedimensional superconformal field theory, chernsimons theory, and their correspondence thesis by hee joong chung in partial ful llment of the requirements for the degree of doctor of philosophy california institute of technology pasadena, california 2014 defended may 30, 2014. The gso projected superconformal field theory spin model with boundary is studied. Selfdual vertex operator superalgebras and superconformal. In the case of scfts constructed from pure gauge theories without matter n 2 n2 n 2 critical points seem to be classified according to the ade. The quantum version of the monodromy matrix, generating quantum im, associated with the susy n 1 kdv is constructed via vertex operator. Type iib superstring theory on ads5 s5 is dual to a scft in 4d n 4 sym theory. Edward witten, fivebrane effective action in mtheory j.
This chapter discusses a new tool called amaximization developed by intriligator and wecht. Petersburg department of steklov mathematical institute, fontanka, 27, 191023 st. Cwill be guided by the parametrization of the conifold c in terms of a1, a2, b1, b2 given in 12. The boundary ward identity for this theory is written and the boundary states for fermionic and spin models are constructed. Its role, if any, in string theorymtheory is still unclear. Superconformal field theories, multiplet shortening, and the ads5. We conjecture that compactifications of mstring theory on various antidesitter spacetimes is dual to various conformal field theories. We present an operator algebraic approach to superconformal. Instantons and 2d superconformal field theory springerlink. From operator algebras to superconformal field theory.
Edward witten, fivebrane effective action in m theory j. This leads to a new proposal for a definition of mtheory which could be extended to include five noncompact dimensions. Making use of the exact solutions of the n 2 n2 n 2 supersymmetric gauge theories we construct new classes of superconformal field theories scfts by finetuning the moduli parameters and bringing the theories to critical points. Instantons and 2d superconformal field theory article pdf available in journal of high energy physics 99 june 2011 with 21 reads how we measure reads. A notion of reflection is introduced which, in special circumstances, produces a vertex operator superalgebra. See at supersymmetry classification superconformal algebra in dimension 2. These authors argued that the elliptic genus of the. Amaximization these slides are based on a guest lecture by brian wecht. Sixdimensional superconformal field theories and their.
In theoretical physics, the sixdimensional 2,0 superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. An extremal n2 superconformal field theory by phil brown on november 14, 2017 researchers at stanford and boston university construct two dimensional cfts with the right properties to be holographic duals of threedimensional supergravity. We study the large n limit of the interacting superconformal field theories associated with n m5 branes or m2 branes using the recently proposed relation between these theories and m theory on ads. Threedimensional superconformal field theory, chernsimons. Superconformal field theory and operator algebras yasuyuki kawahigashi abstract. Pdf n 2 superconformal field theory and noncommutative.
Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, gstructures, and isometry groups. However, considering mtheory configuration giving the 3d3d correspondence and also other several developments, the. In last part of the talk, i will also summarize the exciting recent developments including my own work on the subject. The neveuschwarz and ramond algebras of logarithmic. Ironically, they discovered a beautiful theory that is not the desired dual of mtheory on ads4 s7. The first indication of a 6d theory with a selfdual 2form field appears in. The first half summarizes various aspects of 6d field theories, while the latter half investigates torus compactifications of these theories, and relates them to fourdimensional superconformal field theories in the class, called class s. The firstorder formalism is found by starting from the canonical covariant one. 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. The large n limit of superconformal field theories and supergravity. Superconformal field theory 493 natural realization of such theories is in terms of a complex superfield, and there are four continuously variable parameters corresponding to the metric and torsion which define the toroidal compactification of the bosonic components of the superfield. As we take the decoupling limit we bring the branes together but the the higgs expectation values corresponding to this separation remains. Doing so, we obtain universal bounds and exact relations of n 8 superconformal field theory data. Topological twist in n2 superconformal field theory, i thu, mar 30, 2017 3.
1326 174 615 1183 812 1273 589 270 638 245 458 1517 498 472 1501 177 527 312 310 1267 447 1507 1012 1268 50 960 509 1105 1605 732 1227 1205 25 908 5 246 1360 753 762 215 1271