Geometrical Approaches to Particle Phenomenology: from String Compactification to Supersymmetric Gauge Theories
Lead Research Organisation:
City, University of London
Department Name: Sch of Engineering and Mathematical Sci
Abstract
The eyes of the physics community are turning toward Geneva. In about a year or, the largest particle accelerator and indeed the largest machine known to man, will be turned on. Its purpose, is to smash particles at such a speed and energy that we would be taking a glimpse at the sub-atomic world in a hitherto unfathomed clarity. Data will stream in at an alarming rate. Are we prepared? In a way, we have been preparing for two decades. Since a golden era of particle physics in the 60's nad 70's, what is known as the Standard Model (SM) has been measured and tested to breathtaking accuracy in its description of the microcosm of elementary particles. However, there is a catch. The SM has a number of arbitrary parameters which hint at a more natural, unified theory. More seriously, the SM, in all its glory, has encountered uncurable problems in being compatible with the theory of gravity, the force responsible for the macrocosmic world. Is there a unified theory? Albert Einstein, with prophetic vision, had spent the last of his years trying desperately to find this theory. In comes String Theory. By the mid-80's it was realised that this theory, constituting a fundamental paradigm shift in understanding physics, was a natural unification of gravity with the SM, of the large-scale with the small-scale. It proposes that all particles are different vibration modes of tiny strings, different notes, if you will, of a cosmic symphony. In this symphony, all forces, all interactions, all particles, and indeed all space and time, harmoniously unify. Again, there is a catch. The theory only makes sense in 10 dimensions, as opposed to the three plus one (for time) with which we are familiar. Moreover, the strings are so small that we may never be able to directly detect them. My research is on where the missing 6 dimensions are (after all, 10 minus 4 is equal to 6), what are their properties, and, indeed, how they determine the world we see, assuming that string theory were to be the unified theory of everything. These extra dimensions curl up in specific geometric ways and I have been involved in applying the cutting-edge results from the mathematicians, from the higher-dimensional geometers, to constructing theories which resemble (or, hopefully, exactly reproduce) the SM. The theories which we produce, from these 6-dimensional spaces, all have a special property which is yet to be observed. This is called supersymmetry. It is a proposal that every elementary particle we have thus far seen, comes with a 'super'-partner yet to be been. I have been studying how to obtain a supersymmetric version of the SM from string theory and have had some success. Earlier this year, my collaborators and I have found a special 6-dimensional geometry which gives just the right particles! We know that such geometry is rare since of the thousands of models constructed from string theory and of the infinite number of possibilities for the 6-dimensional space, this is the only one that has exactly the right particles, no more and no less. There remains much to be done. We must work out the details of this model and especially ascertain how special our geometry is and whether there are other possibilities. A key goal of the machine at Geneva is to test signatures of supersymmetry. Checking our model against the influx of data is of vital importance. The Theoretical Physics Department at Oxford is a unique place, in that it has some of the founding members who initiated this study of trying to bring string theory to produce the SM interaction of particles, and in that it neighbours the Mathematical Institute, which is a world center for geometry. With these members of both departments I am currently collaborating. The dynamic interaction is precisely geared to my using the latest advanced in geometry to answer perhaps most pressing issue of particle physics, in light of the Geneva data: 'how does string theory produce the SM?'
People |
ORCID iD |
Yang-Hui He (Principal Investigator / Fellow) |
Publications
Anderson L
(2010)
Exploring positive monad bundles and a new heterotic standard model
in Journal of High Energy Physics
Anderson L
(2010)
Yukawa Couplings in Heterotic Compactification
in Communications in Mathematical Physics
Benishti N
(2010)
(Un)Higgsing the M2-brane
in Journal of High Energy Physics
Braun V
(2013)
Supersymmetric hidden sectors for heterotic standard models
in Journal of High Energy Physics
Duncan M
(2014)
The statistics of vacuum geometry
in Journal of High Energy Physics
Franco S
(2012)
Towards the continuous limit of cluster integrable systems
in Journal of High Energy Physics
Gray J
(2012)
Necessary conditions on Calabi-Yau manifolds for large volume vacua
in Physical Review D
Hanany A
(2011)
The beta ansatz: a tale of two complex structures
in Journal of High Energy Physics
HANANY A
(2012)
INVARIANTS OF TORIC SEIBERG DUALITY
in International Journal of Modern Physics A
Description | I continued to develop the interactions between geometry, number theory and the physics of high energies. This caught the attention of Fields Medalist Prof. Shing-Tung Yau of Harvard with whom I finished a publication and the famous mathematician Prof. John McKay of Canada, with whom I have now 3 papers. In total, while holding this STFC grant over the 5 years between 2008-2013 I have generated 49 journal papers with over 2000 citations for them, as well as given over 50 lecture series, colloquia, seminars and public/outreach lectures. |
Exploitation Route | The interactions amongst these diverse topics should be of use to string theorist, field theories as well as pure mathematicians. |
Sectors | Education |
Description | Hanany Group |
Organisation | Imperial College London |
Department | Department of Physics |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | This is a long-term collaboration, ever since I was Prof. Hanany's PhD student. He has moved to London and we continue to work closely on the interface between geometry, combinatorics and gauge theories. |
Collaborator Contribution | We have had fruitful collaborations over many years with Prof. A. Hanany, which continues today, and being particularly active now since I moved to London last year |
Impact | Many PhD students, Masters students, and dozens of papers have been produced in the collaboration. |
Description | Harvard University: Prof Yau |
Organisation | Harvard University |
Country | United States |
Sector | Academic/University |
PI Contribution | I have started a collaboration with Professor S-T Yau, Fields Medalist and the founder the subject of Calabi-Yau manifolds since 2013. We have 2 papers since then, both published in the prestigious journal Communicationss in Mathematical Physics |
Collaborator Contribution | Prof Yau is a world-renowned figure in geometry and mathematical physics. |
Impact | 1) Calabi-Yau Volumes and Reflexive Polytopes. By Yang-Hui He, Rak-Kyeong Seong, Shing-Tung Yau. [arXiv:1704.03462 [hep-th]]. 10.1007/s00220-018-3128-6. Commun. Math. Phys. (2018). 2) Extremal Bundles on Calabi-Yau Threefolds. By Peng Gao, Yang-Hui He, Shing-Tung Yau. [arXiv:1403.1268 [hep-th]]. 10.1007/s00220-014-2271-y. Commun.Math.Phys. 336 (2015) no.3, 1167-1200. |
Start Year | 2013 |
Description | Northeastern |
Organisation | Northeastern University - Boston |
Department | Department of Physics |
Country | United States |
Sector | Academic/University |
PI Contribution | Last year we received a joint grant with Prof. B. Nelson of Northeastern University from the NSF |
Collaborator Contribution | We are establishing a new programming of using parallel computing in high energy physics |
Impact | We, together with two co-PIs, Dr. Jejjala and Dr. Gray, have just hired a new postdoc, to use the Cloud Parallel Computing Paradigm for the sake of particle and string phenomenology. This should carry on for the next 3 years. |
Start Year | 2010 |
Description | Oxford Group: Mathematics |
Organisation | University of Oxford |
Department | Mathematical Institute Oxford |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | We are using cutting-edge results in algebraic geometry to understand Calabi-Yau compatifications |
Collaborator Contribution | I have been working closely with Prof. P. Candelas, Dr. de la Ossa and Dr. Szendroi, a collaboration continuing today |
Impact | Again, whilst in Oxford with my Advanced Fellowship with the STFC, we produced 17 papers between 2008 till 2010 when I left Oxford. |
Start Year | 2006 |
Description | Oxford Group: Physics |
Organisation | University of Oxford |
Department | Rudolf Peierls Centre for Theoretical Physics |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | I have been a co-founder, with Prof. Andre Lukas, of the algorithmic phenomenology group within the Oxford Theoretical Physics sub-department where I was working when I first received the STFC Advanced Fellowship. |
Collaborator Contribution | We investigated together the algorithms in string and particle phenomenology |
Impact | During the period of 2008 (when I first received the STFC advanced fellowship) till present, we have produced 17 papers on related subjects, and 4 PhD students, two my own |
Start Year | 2007 |
Description | Queen Mary, University of London |
Organisation | Queen Mary University of London |
Department | School of Physics and Astronomy |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | I have been computing new invariants hitherto unrealised in the direction of dualities. |
Collaborator Contribution | we are make good progress in the direction of field theories |
Impact | We in process of publishing several papers this year |
Start Year | 2011 |
Description | UCL |
Form Of Engagement Activity | Participation in an open day or visit at my research institution |
Part Of Official Scheme? | Yes |
Primary Audience | Public/other audiences |
Results and Impact | Presented a popular talk on the history of mathematics to the historical UCL chemical society much enthusiastic response from chemists about the pure beauties of group theory |
Year(s) Of Engagement Activity | 2010 |