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Higher Spins & Strings and Mathieu Moonshine

English title Higher Spins & Strings and Mathieu Moonshine
Applicant Gaberdiel Matthias
Number 165667
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 01.04.2016 - 31.03.2019
Approved amount 600'000.00
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All Disciplines (3)

Discipline
Theoretical Physics
Mathematics
Particle Physics

Keywords (3)

Higher Spin Theory; Conformal Field Theory; String Theory

Lay Summary (German)

Lead
Die Höhere Spintheorie/CFT Dualität und Mathieu Moonshine.
Lay summary
Eine der wichtigsten Einsichten in der String Theorie der letzten Jahre ist die Erkenntnis, dass String Theorie auf einem d-dimensionalen Anti-de-Sitter Hintergrund zu einer konformen Feldtheorie (CFT) in (d-1) Dimensionen äquivalent ist. Diese sogenannte AdS-CFT Dualität ist von grosser Bedeutung, da viele interessante Grössen, die zum Beispiel vom Standpunkt der String Theorie nur schwer berechenbar sind, eine einfache Beschreibung in der dualen konformen Feldtheorie haben (und umgekehrt). 
Diese Dualität ist in vielen Fällen erfolgreich überprüft worden; allerdings fehlt bislang ein Beweis für sie. Man erwartet, dass die Dualität in einem Spezialfall (nämlich, wenn die Stringspannung verschwindend klein ist) sich zu der Dualität zwischen einer sogenannten Höheren Spintheorie und einer fast freien dualen konformen Feldtheorie vereinfacht. Ziel des Projektes ist es die AdS-CFT Dualität von diesem Standpunkt aus zu analysieren. Dieser Gesichtspunkt könnte es einem insbesondere erlauben, die Dualität zumindest in diesem Spezialfall zu beweisen.
 
Ein zweites Ziel des Projektes ist es, das Auftreten der Mathieugruppe M24 im elliptischen Genus von K3 mikroskopisch zu erklären. 
Direct link to Lay Summary Last update: 29.03.2016

Responsible applicant and co-applicants

Employees

Publications

Publication
Long strings and chiral primaries in the hybrid formalism
Eberhardt Lorenz, Ferreira Kevin (2019), Long strings and chiral primaries in the hybrid formalism, in Journal of High Energy Physics, 2019(2), 98-98.
Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model
Dei A., Sfondrini A. (2019), Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model, in Journal of High Energy Physics, 2019(2), 72-72.
The plane-wave spectrum from the worldsheet
Eberhardt Lorenz, Ferreira Kevin (2018), The plane-wave spectrum from the worldsheet, in Journal of High Energy Physics, 2018(10), 109-109.
N = (3, 3) holography on AdS3 × (S3 × S3 × S1)/ℤ2
Eberhardt Lorenz, Zadeh Ida G. (2018), N = (3, 3) holography on AdS3 × (S3 × S3 × S1)/ℤ2, in Journal of High Energy Physics, 2018(7), 143-143.
Integrable spin chain for stringy Wess-Zumino-Witten models
Dei A., Sfondrini A. (2018), Integrable spin chain for stringy Wess-Zumino-Witten models, in Journal of High Energy Physics, 2018(7), 109-109.
Probing Wigner rotations for any group
Oblak Blagoje (2018), Probing Wigner rotations for any group, in Journal of Geometry and Physics, 129, 168-185.
Near-horizon extremal geometries: coadjoint orbits and quantization
Javadinezhad R., Oblak B., Sheikh-Jabbari M. M. (2018), Near-horizon extremal geometries: coadjoint orbits and quantization, in Journal of High Energy Physics, 2018(4), 25-25.
Thomas precession for dressed particles
Oblak Blagoje (2018), Thomas precession for dressed particles, in Classical and Quantum Gravity, 35(5), 054001-054001.
Supersymmetric AdS3 supergravity backgrounds and holography
Eberhardt Lorenz (2018), Supersymmetric AdS3 supergravity backgrounds and holography, in Journal of High Energy Physics, 2018(2), 87-87.
Higher spin algebras and large N=4 holography
Eberhardt Lorenz, Gaberdiel Matthias R., Rienacker Ingo (2018), Higher spin algebras and large N=4 holography, in JHEP, 03, 097-097.
Stringy N=(2,2) holography for AdS3
Datta Shouvik, Eberhardt Lorenz, Gaberdiel Matthias R. (2018), Stringy N=(2,2) holography for AdS3, in JHEP, 01, 146-146.
Tensionless string spectra on AdS3
Gaberdiel Matthias R., Gopakumar Rajesh (2018), Tensionless string spectra on AdS3, in JHEP, 05, 085-085.
The plane-wave limit of AdS3×S3×S3×S1
Dei Andrea, Gaberdiel Matthias R., Sfondrini Alessandro (2018), The plane-wave limit of AdS3×S3×S3×S1, in Journal of High Energy Physics, 097.
The supersymmetric affine Yangian
Gaberdiel Matthias R., Li Wei, Peng Cheng, Zhang Hong (2018), The supersymmetric affine Yangian, in JHEP, 05, 200-200.
Twin-plane-partitions and N=2 affine Yangian
Gaberdiel Matthias R., Li Wei, Peng Cheng (2018), Twin-plane-partitions and N=2 affine Yangian, in JHEP, 11, 192-192.
Berry Phases on Virasoro Orbits
Oblak Blagoje (2017), Berry Phases on Virasoro Orbits, in Journal of High Energy Physics, 1710, 114.
Even spin N = 4 holography
Ferreira Kevin (2017), Even spin N = 4 holography, in Journal of High Energy Physics, 1709, 110.
A holographic dual for string theory on AdS3 × S3 × S3 × S1
Eberhardt Lorenz, Gaberdiel Matthias, Li Wei (2017), A holographic dual for string theory on AdS3 × S3 × S3 × S1, in Journal of High Energy Physics, 1708, 111.
Stringy AdS3 from the Worldsheet
Gaberdiel Matthias, Gopakumar Rajesh, Hull Chris (2017), Stringy AdS3 from the Worldsheet, in Journal of High Energy Physics, 1707, 90.
BPS spectrum on AdS3×S3×S3×S1
Eberhardt Lorenz, Gaberdiel Matthias, Gopakumar Rajesh, Li Wei (2017), BPS spectrum on AdS3×S3×S3×S1, in Journal of High Energy Physics, 1703, 124.
Higher Spins and Yangian Symmetries
Gaberdiel Matthias R., Gopakumar Rajesh, Li Wei, Peng Cheng (2017), Higher Spins and Yangian Symmetries, in JHEP, 04, 152-152.
Higher spins on AdS3 from the worldsheet
Ferreira Kevin, Gaberdiel Matthias R., Jottar Juan I. (2017), Higher spins on AdS3 from the worldsheet, in JHEP, 07, 131-131.
Mathieu Moonshine and Symmetry Surfing
Gaberdiel Matthias, Keller Christoph, Paul Hynek (2017), Mathieu Moonshine and Symmetry Surfing, in Journal of Physics A, 50, 474002.
Twisted sectors from plane partitions
Datta Shouvik, Gaberdiel Matthias, Li Wei, Peng Cheng (2016), Twisted sectors from plane partitions, in Journal of High Energy Physics, 1609, 138.

Collaboration

Group / person Country
Types of collaboration
Prof. Marcos Marino, University of Geneva Switzerland (Europe)
- Research Infrastructure
Dr. Cheng Peng, Brown University United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Peter Goddard United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Rajesh Gopakumar, ICTS Bangalore India (Asia)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Chris Hull, Imperial College London Great Britain and Northern Ireland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Matthias Blau, Universität Bern Switzerland (Europe)
- Research Infrastructure
Prof. Wei Li, ITP, Chinese Academy of Science China (Asia)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Integrability and Conformal Field Theory 2019 Talk given at a conference The integrable structure of stringy AdS3 WZW model 29.03.2019 Oxford , Great Britain and Northern Ireland Dei Andrea;
Higher spins and holography Talk given at a conference Tensionless strings on AdS3 20.03.2019 ESI Vienna, Austria Eberhardt Lorenz Valentin;
Chaos, Holography and Coadjoint Orbits Talk given at a conference Virasoro Berry Phases in the KdV Equation 01.03.2019 Geneva, Switzerland Oblak Blagoje;
Avant-garde methods for QFT and Gravity Talk given at a conference Higher Spins & Strings on AdS3 21.02.2019 Nazareth, Israel Gaberdiel Matthias;
Holomorphic Differentials in Mathematics and Physics Poster A combinatorial approach to saddle-counting invariants for quadratic differentials 04.02.2019 Simons Center for Geometry and Physics, Stony Brook University, NY, United States of America Longhi Pietro;
Higher symmetries and Quantum Gravity Talk given at a conference The higher spin square and its emergence from the worldsheet 07.12.2018 Max Planck Institute for Gravitational Physics, Potsdam, Germany Eberhardt Lorenz Valentin;
DESY Theory Workshop, Particle Physics Challenges Talk given at a conference The spin chain for the AdS3 WZW model 27.09.2018 Hamburg, Germany Dei Andrea;
Conference on Geometry and Strings Talk given at a conference AdS3 at the string scale 27.07.2018 Ringberg Castle , Germany Gaberdiel Matthias;
New Frontiers in String Theory 2018 Talk given at a conference AdS3 at the string scale 03.07.2018 YITP Kyoto, Japan Gaberdiel Matthias;
AdS/CFT at 20 and Beyond Talk given at a conference AdS3 at the string scale 28.05.2018 ICTS Bangalore, India Gaberdiel Matthias;
String Theory and Quantum Gravity Talk given at a conference Berry Phases of Boundary Gravitons 03.07.2017 Ascona, Switzerland Oblak Blagoje;
Recent Trends in String Theory and Related Topics Talk given at a conference Berry Phases of Boundary Gravitons 08.05.2017 Teheran, Iran Oblak Blagoje;
New Developments in AdS3/CFT2 holography Talk given at a conference Strings on AdS3xS3xS3xS1 03.05.2017 GGI Florence, Italy Eberhardt Lorenz Valentin;
The String Theory Universe Talk given at a conference BPS states in AdS3 ×S3 ×S3 ×S1 20.02.2017 Milano, Italy Gaberdiel Matthias;
The String Theory Universe Poster BMS Particles in Three Dimensions 20.02.2017 Milano, Italy Oblak Blagoje;
The First Mandelstam Theoretical Physics School and Workshop: Recent Advances in AdS/CFT Talk given at a conference Higher Spin AdS / CFT duality 11.01.2017 Durban, South Africa Gaberdiel Matthias;
Strings 2016 Talk given at a conference Higher Spin Algebras & Plane Partitions 01.08.2016 Tsinghua University, China Gaberdiel Matthias;
Aspects of Higher Spin Theory Talk given at a conference The structure of the stringy higher spin algebra 23.05.2016 MIAPP Munich, Germany Gaberdiel Matthias;


Self-organised

Title Date Place
String Theory and Quantum Gravity 03.07.2017 Monte Verita, Ascona, Switzerland

Awards

Title Year
CSF award for best talk at conference "String Theory and Quantum Gravity", Ascona, 3-7 July 2017. 2017

Associated projects

Number Title Start Funding scheme
184841 Exact AdS/CFT dualities and Mathieu Moonshine 01.04.2019 Project funding (Div. I-III)
146186 The Higher Spin AdS/CFT correspondence and Mathieu Moonshine 01.04.2013 Project funding (Div. I-III)

Abstract

One of the most important topics in string theory in recent years has been the AdS/CFT correspondence. In its original form it relates string theory on a 5-dimensional Anti-de Sitter background to N=4 superconformal Yang-Mills theory in 4 dimensions. This duality is of great importance since it allows one to gain insight into quantum gravity on the one hand, and into strongly coupled (gauge) theories on the other. Unfortunately, however, a real understanding of why this correspondence works and which ingredients are crucial for its functioning is still missing. This is an important question given that for many interesting applications of the AdS/CFT correspondence, say to QCD or condensed matter physics, other versions of the duality (that cannot be directly justified from string theory) seem to be relevant. In order to gain insight into this problem it is instructive to consider the limit in which the conformal field theory is weakly coupled. In that case, the dual string theory is believed to possess a consistent higher spin subsector that should be dual to the nearly free field theory. This special case is of quite some interest since both sides of the duality are then weakly coupled, and hence one may hope to find a perturbative proof of the AdS/CFT correspondence in this regime. It may also allow one to get a glimpse of the large symmetry that is believed to underlie string theory.About five years ago I made (together with Rajesh Gopakumar) a concrete proposal for such a duality. It relates a specific higher spin theory on AdS3 to a 't Hooft like large N limit of a family of 2-dimensional minimal model conformal field theories. By now substantial support for this proposal has been obtained, and recently the precise connection with string theory has been understood. This has opened the door for a number of interesting problems: in particular, it should be possible to exhibit in detail the structure of the symmetry algebra underlying string theory at its most symmetrical point (the tensionless point), to understand the constraints of this symmetry for various aspects of the theory, and to unravel the relation of these symmetries to the integrable structure that is, for example, visible in the spin-chain approach. Finally, since the duality is also understood in detail at finite N, the 2d CFT makes concrete predictions for quantum gravity effects in AdS3, which it would be very interesting to understand from a perturbative quantum gravity point of view. All of these directions (as well as others in this area) will be pursued. In 2010, Eguchi, Ooguri, and Tachikawa observed that the first few Fourier coefficients of the elliptic genus of K3 can be written in terms of dimensions of Mathieu M24 representations. (The Mathieu group M24 is one of the sporadic finite simple groups.) In previous work I have given very convincing evidence that this observation is true for all Fourier coefficients, and it would be very interesting to understand the microscopic origin of this fact.
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