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Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

English title | The AdS/CFT correspondence, pure spinors and logarithmic conformal field theories |
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Applicant | Gaberdiel Matthias |

Number | 129542 |

Funding scheme | Project funding (Div. I-III) |

Research institution | Institut für Theoretische Physik ETH Zürich |

Institution of higher education | ETH Zurich - ETHZ |

Main discipline | Theoretical Physics |

Start/End | 01.04.2010 - 31.03.2013 |

Approved amount | 559'276.00 |

Discipline |
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Theoretical Physics |

Mathematics |

String Theory; Conformal Field Theory

Lead |
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Lay summary |

String theory is currently the most promising candidate for a unifying framework to describe all known interactions. These include, in particular, the `standard model' of particle physics as well as Einstein's theory of gravity, general relativity. The basic idea of string theory is that the fundamental object is a one-dimensional string (rather than a point-like object). The different elementary particles correspond to the different ways in which this string can vibrate in the ambient spacetime. On the other hand, Einstein's equations of general relativity appear as consistency conditions. As the string propagates through spacetime it sweeps out a two-dimensional surface, the world-sheet. From the point of view of this world-sheet, the vibrations of the string can be described in terms of a two-dimensional conformal field theory.One of the most dramatic recent progress in string theory concerns the so-called AdS/CFT correspondence. It proposes that strings propagating on an anti-de-Sitter (AdS) spacetime are in fact equivalent to conventional (conformal) quantum field theories. It is one of the key aims of this project to develop the world-sheet formulation of string theory on AdS spacetimes further, in particular using the pure spinor formulation of string theory. This would allow one to test and understand this correspondence in more detail. Conformal field theories also play an important role for the description of critical phenomena in statistical physics. In recent years, logarithmic conformal field theories have increasingly attracted attention since they are, for example, relevant for systems with quenched disorder. It is another aim of this project to study such logarithmic theories from a first principle conformal field theory perspective. |

Direct link to Lay Summary | Last update: 21.02.2013 |

Name | Institute |
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Name | Institute |
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Publication |
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Even spin minimal model holography |

Gravity dual of the Ising model |

Higher spin black holes from CFT |

Limits of minimal models and continuous orbifolds |

Limits of minimal models and continuous orbifolds |

String states on AdS3 x S3 from the supergroup |

Symmetries of K3 sigma models |

Triality in minimal model holography |

A modular invariant bulk theory for the c=0 triplet model |

An AdS(3) dual for minimal model CFTs |

Borcherds algebras and N=4 topological amplitudes |

Enhanced gauge groups in N=4 topological amplitudes and Lorentzian Borcherds algebras |

Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces |

Minimal model holography for SO(2N) |

On the topology of the hypermultiplet moduli space in type II/CY string vacua, |

Partition functions of holographic minimal models |

Quantum W-symmetry in AdS(3) |

Symmetries of holographic minimal models |

The massless string spectrum on AdS(3) x S-3 from the supergroup |

Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence |

Graviton 1-loop partition function for 3-dimensional massive gravity |

Mathieu Moonshine in the elliptic genus of K3 |

Mathieu twining characters for K3 |

The heat kernel on AdS(3) and its applications |

Title | Type of contribution | Title of article or contribution | Date | Place | Persons involved |
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Higher Spin Theories and Holography | Talk given at a conference | 3 Lectures on Minimal Model Holography | 23.11.2011 | Allahabad, India | Gaberdiel Matthias; |

Conformal ﬁeld theory, automorphic forms, and related topics | Talk given at a conference | Mathieu Moonshine | 19.09.2011 | Heidelberg, Germany | Gaberdiel Matthias; |

Advanced Conformal Field Theory and Application | Talk given at a conference | Fusion in (Logarithmic) Conformal Field Theory | 05.09.2011 | IHP Paris, France | Gaberdiel Matthias; |

Title | Date | Place |
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Higher Spins, Strings and Duality | 18.03.2013 | GGI Florence, Italy |

Integrability and Gauge & String Theory | 20.08.2012 | ETH Zurich, Switzerland |

Workshop on Higher Spin Gravity | 10.04.2012 | ESI Wien, Austria |

Strings, M-Theory & Quantum Gravity | 25.07.2011 | Monte Verita, Switzerland |

Mathieu Moonshine | 07.07.2011 | ETH Zurich, Switzerland |

Number | Title | Start | Funding scheme |
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146186 | The Higher Spin AdS/CFT correspondence and Mathieu Moonshine | 01.04.2013 | Project funding (Div. I-III) |

119830 | String moduli, the AdS/CFT correspondence and logarithmic conformal field theories | 01.04.2008 | Project funding (Div. I-III) |

String theory is currently the most promising candidate for a unifying framework to describe the standard model of particle physics as well as general relativity. One of the areas where most progress has been achieved during the last few years is the AdS/CFT correspondence. In its simplest incarnation it relates string theory on AdS5xS5 to a supersymmetric quantum field theory in four dimensions. The correspondence has helped to shed light on the structure of N = 4 super Yang-Mills theory, and it has led to interesting applications for plasma physics and in condensed matter theory. However, one of the key obstacles towards further progress is that a tractable world-sheet description for strings on AdS5xS5 is so far lacking. There are various ideas for how to make progress with this problem, in particular the pure spinor formulation of Berkovits, as well as the reconstruction programme of Gopakumar. I plan to pursue both of these approaches. In a somewhat separate development, Witten has recently proposed that the AdS/CFT dual of pure gravity in AdS3 is described by an extremal self-dual conformal field theory. A related proposal was subsequently put forward by Strominger and coworkers. In either case, depending on the value of the cosmological constant of the AdS space, the conformal field theories have central charge c = 24k, where k = 1, 2, 3, ... The first theory at c = 24 (k = 1) is the famous Monster conformal field theory, but the theories for k > 1 have so far not been constructed. In the last two years I have given various arguments that suggests that these `extremal' theories are inconsistent for large k. However, the issue has not yet been completely settled, and I would like to use the analysis of higher genus amplitudes to study this problem further.The world-sheet of the string is described by a two-dimensional conformal field theory. Such theories also play an important role for the description of critical phenomena in two dimensions. One class of conformal field theories that have recently attracted a lot of attention are the so-called logarithmic conformal field theories. They appear in various models of statistical physics, for example in the theory of polymers, percolation and various disordered models. They probably also play an important role in Strominger's modification of the pure gravity proposal of Witten. Recently, significant progress (partially by myself) has been made in the general study of logarithmic conformal field theories, but much more remains to be understood. Among other things I want to study logarithmic conformal field theories at c = 0 that are believed to be important for critical systems with quenched disorder.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

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