# Precision calculations in field theories and in string theory and the relations between them

Lead Research Organisation:
Imperial College London

Department Name: Dept of Physics

### Abstract

My field of research is string theory, a very advanced theoretical construct that allows for the unification of all the forces of nature. String theory has different limits, in some the dominant effects are gravitational and in others they are field-theoretical. The application of string theory as a unified theory of nature is not mature yet, but is a very exciting possibility. Until the day comes when we can use strings to make experimental predictions we try to gain a better understanding of the theory and try to learn from it about other questions in theoretical physics. That is the direction I pursue in my research. As stated above, we can isolate from string theory some subsectors, which are described by simpler theories. In particular, what are known as gauge theories (the simplest of which is elecro-magnetism). The realm of subatomic particles is well described by one such theory (know as ``the standard model of particle physics''). This theory can be realized in string theory by rather complicated constructions. There is another gauge theory with a beautifully simple realization in string theory, commonly known as N=4 supersymmetric Yang-Mills. The simple manifestation of this theory in string theory allows us to make precise calculations both at strong and weak coupling and compare the results, often with surprising agreement. While this theory is probably not realized in nature, it is similar in many ways to the standard model of particle physics. A better understanding of this theory should lead to better calculational tools for particle physics. While this theory is simpler (in some ways) than the standard model, it is still quite rich and complicated. My specific research focuses on identifying subsectors of the theory where exact results can be obtained. Several such subsectors are known (and I have contributed to their understanding) and the purpose of my research is to find more such subsectors, understand the known ones better and enlarge them to include more calculable quantities. The ultimate goal of this line of research is to have a complete understanding of this theory, where all quantities can be calculated. This goal seems quite far from being attained at the moment, but remarkable progress has been achieved over the past few years that gives hope that this goal is not completely out of reach. Whether we reach that target or not, a better understanding of this theory promises to have other applications in theoretical physics. It could have applications in other corners of string theory, or even for condensed matter physics, which uses some of the same tools used in studying N=4 Yang-Mills. Furthermore, it could help understand the standard model and in particular QCD, the theory of the strong interactions. That theory is strongly coupled and understanding how other theories behave at strong coupling could shed light on this theory too.

## People |
## ORCID iD |

Nadav Drukker (Principal Investigator / Fellow) |

### Publications

Dabholkar A
(2014)

*Localization in supergravity and quantum AdS 4 /CFT3 holography*in Journal of High Energy Physics
Drukker N
(2011)

*Generalized quark-antiquark potential at weak and strong coupling*in Journal of High Energy Physics
Drukker N
(2011)

*From Weak to Strong Coupling in ABJM Theory*in Communications in Mathematical Physics
Drukker N
(2011)

*The virtue of defects in 4D gauge theories and 2D CFTs*in Journal of High Energy Physics
Drukker N
(2011)

*(de)Tails of Toda CFT*in Journal of High Energy Physics### Related Projects

Project Reference | Relationship | Related To | Start | End | Award Value |
---|---|---|---|---|---|

ST/H005382/1 | 01/10/2010 | 01/10/2011 | £494,053 | ||

ST/H005382/2 | Transfer | ST/H005382/1 | 01/10/2011 | 30/09/2015 | £402,336 |

Description | I have further developed our understanding of field theories, similar to those describing elementary particles and of string theory, which is a unified theory of particles and gravity. In particular I found new quantities that can be evaluated precisely in such theories and evaluated them, applying and developing different tools of theoretical physics. The quantities I calculated capture properties like the number of degrees of freedom of a theory. These exact results can be compared in different theories to find theories relations among them - for example equivalences between string theories and field theories and between seemingly very different field theories. |

Exploitation Route | Absolutely. My publications are cited very highly, indicating that they are useful to others. The outcomes of my calculations are useful as the starting point for other work, or as background information. Likewise the techniques I developed to perform the calculations have proven extremely useful to many other researchers, who employed them for their problems and developed them further. |

Sectors | Education |

Description | ABJM |

Organisation | University of Geneva |

Department | Section of Mathematics |

Country | Switzerland |

Sector | Academic/University |

PI Contribution | I've collaborated with Members of the University of Geneva in writing a manuscript to be submitted to a journal soon. |

Collaborator Contribution | We collaborated on writing a paper and they invited me to Geneva for that purpose for a week. |

Impact | two papers: Commun.Math.Phys. 306 (2011) 511-563 and JHEP 1111 (2011) 141 |

Start Year | 2009 |

Description | AGT |

Organisation | Humboldt University of Berlin |

Department | Institute of Physics |

Country | Germany |

Sector | Academic/University |

PI Contribution | I've collaborated on the project with Filippo Passerini. |

Collaborator Contribution | I have collaborated with a member of Humboldt University in Berlin on writing a paper which is out as a preprint and in the process of being refereed for JHEP. We are currently collaborating on several further projects. |

Impact | paper: JHEP 1104 (2011) 106 |

Start Year | 2010 |

Description | quark-antiquark |

Organisation | Max Planck Society |

Department | Max Planck Institute for Gravitational Physics |

Country | Germany |

Sector | Academic/University |

PI Contribution | I've been working with a member of the Max Planck Institute in Golm on a project to study the quark antiquark potential in gauge theory and string theory. |

Collaborator Contribution | We are collaborating on a project to be completed soon. |

Impact | paper: JHEP 1106 (2011) 131 and proceeding: Fortsch.Phys. 60 (2012) 1019-1025 |

Start Year | 2010 |