# Lattice Gauge Theories beyond QCD: large N, Supersymmetry and Orientifold planar equivalence

Lead Research Organisation:
Swansea University

Department Name: College of Science

### Abstract

Among the fundamental interactions (strong, electroweak and gravitational). the strong interactions are probably the most elusive. Although they do not manifest themselves directly in the macroscopic world, strong interactions account for the stability of matter, since they are responsible for forces that bind neutrons and protons inside nuclei. Neutrons and protons are members of a wider family of particles, the hadrons, all of which interact strongly. The hadrons are not elementary particles: they are made of more fundamental particles, quarks and gluons. In electromagnetism particles interact through their electric charge; in strong interactions particles interact through a charge which this time is called pictorially colour. In nature there are three different colour charges; we speak then of the red, blue and green quarks, referring by the colour to the particular charge carried by a particle (which has nothing to do with the colours we see in our everyday experience). The theory that describes quark, gluons and their interaction is QCD. Currently, QCD (whose fine details are going to be tested at LHC) is not fully understood: while we have clear analytical predictions for the high energy regime (energies of 1 GeV or more), analytical computation techniques we currently know can not be used in the low energy regime. Unfortunately this is the most interesting regime, since e.g. quarks inside nucleons have low energies. In the absence of analytical predictions, a successful numerical approach has been developed: Monte Carlo based simulations of the theory discretised on a lattice. In this approach, the theory is formulated on a discrete and finite spacetime of spacing a and linear dimension L. This simplified theory is formulated in terms of a finite number of integrals, which can be performed on a (super)computer. The continuous theory is recovered by extrapolating to the limits L going to infinity and a going to zero. In order to fully exploit the predictive power of the calculations, an analytical understanding is still needed. Much progress has been achieved on this side by considering QCD as a special case of a more general class of theories. One possibility in this sense is to take the large N limit for a SU(N) gauge theory coupled to quarks. QCD is recovered when N=3. The large N theory is simpler than the original N=3 one, and corrections to it due to a finite value of N can be expressed as a power series in 1/N. Recently the lattice has proved to be an useful tool for determining the unknown coefficients of that power series in the absence of quarks. We plan to extend that work also when Nf quarks are included in the theory. Another interesting direction is the Orientifold planar equivalence. This is a different large N limit that relates theories with generalised quarks: a SU(N) gauge theory with an antisymmetric quark on one side and a SU(N) gauge theory with an adjoint quark on the other. The predictive power of this framework is due to the fact that the latter is related to N=1 Super Yang-Mills, for which much is know analytically, while the former reduces to QCD with one quark when N=3. Open questions remain, like the size of the corrections to recover QCD with the correct number of flavours or to go from the infinite N case to N=3. One of the central points of our project is to answer those questions. This will require a non-trivial generalisation of currently used lattice QCD algorithms and techniques. Once we have developed the techniques to simulate a generic number of fermions in a generic representation of a SU(N) gauge group, we would have the tools to attack other interesting problems, like N=1 Super Yang-Mills on the lattice and alternative scenarios for the electroweak symmetry breaking mechanism. Both those problems have a high phenomenological relevance, and will be studied at the upcoming LHC experiments.

### Publications

Armoni A
(2008)

*Lattice study of planar equivalence: The quark condensate*in Physical Review D
Armoni A
(2009)

*Degeneracy between the Regge slope of mesons and baryons from supersymmetry*in Journal of High Energy Physics
Del Debbio L
(2010)

*Mesonic spectroscopy of minimal walking technicolor*in Physical Review D
Del Debbio L
(2010)

*Infrared dynamics of minimal walking technicolor*in Physical Review D
Del Debbio L
(2009)

*Conformal versus confining scenario in SU(2) with adjoint fermions*in Physical Review D
Del Debbio L
(2010)

*Higher representations on the lattice: Numerical simulations, SU(2) with adjoint fermions*in Physical Review D
Lucini B
(2010)

*Strongly interacting dynamics beyond the standard model on a space-time lattice.*in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Lucini B
(2009)

*Discrete symmetry breaking and baryon currents in U ( N ) and SU ( N ) gauge theories*in Physical Review D
Lucini B
(2010)

*A numerical investigation of orientifold planar equivalence for quenched mesons*in Physical Review DDescription | The recent discovery of the Higgs boson has advanced our understanding of the standard model of particle interactions. One of the principal roles of the Higgs field is to give mass to the carriers of the weak force. The mechanism through which this happens is called electroweak symmetry breaking. However, theoretical considerations show us that electroweak symmetry breaking through the Higgs field must be an effective mechanism. Hence, a more fundamental explanation is needed. One of the crucial questions in theoretical high energy physics is what is the fundamental mechanism that breaks the electroweak symmetry. Among other conjectures, an open possibility is that the symmetry is broken by a new strong force. We have studied with Monte Carlo calculations on state of the art supercomputers models of strong dynamics, providing solid evidence of the viability of this phenomenon as the fundamental mechanism of electroweak symmetry breaking. |

Exploitation Route | The main beneficiary of our work in the short to medium term is the academic community, which can build on our results to propose new improved models of electroweak symmetry breaking and new experiments to test them. In addition, in order to perform our calculations, we produced an advanced simulation software that is very flexible and can be used for a diverse set of applications requiring supercomputers. As a demonstration, we have produced an advanced benchmarking suite for supercomputers called BSMBench. The tool is currently being commercialised. |

Sectors | Energy,Financial Services, and Management Consultancy,Other |

Description | The core software produced during the project finds various applications in various fields (finance, meteorology etc.) that require performing numerical simulations on state of the art supercomputers |

First Year Of Impact | 2011 |

Sector | Energy,Financial Services, and Management Consultancy,Other |

Impact Types | Economic |

Description | HPC |

Amount | £1,203,993 (GBP) |

Organisation | Science and Technologies Facilities Council (STFC) |

Sector | Public |

Country | United Kingdom |

Start | 10/2010 |

End | 09/2013 |

Description | Responsive mode grants |

Amount | £18,218 (GBP) |

Organisation | Engineering and Physical Sciences Research Council (EPSRC) |

Sector | Public |

Country | United Kingdom |

Start | 04/2009 |

End | 07/2009 |

Description | Royal Society University Research Fellowship (extension) |

Amount | £325,343 (GBP) |

Organisation | The Royal Society |

Sector | Charity/Non Profit |

Country | United Kingdom |

Start | 10/2010 |

End | 09/2013 |

Description | BSM Strong Dynamics |

Organisation | University of Edinburgh |

Department | School of Physics and Astronomy |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | We performed most of the simulations, developed a parallel version of the code, analysed the results and contributed substantially to devising the interpretation of the data. |

Collaborator Contribution | Provide complementary knowledge and contributed computer time. |

Impact | Development of a state of the art code, publications of high-impact articles, applications for further funding. |

Start Year | 2007 |

Description | BSM Strong Dynamics |

Organisation | University of Southern Denmark |

Department | Centre for Cosmology and Particle Physics Phenomenology (CP3-Origins) |

Country | Denmark |

Sector | Academic/University |

PI Contribution | We performed most of the simulations, developed a parallel version of the code, analysed the results and contributed substantially to devising the interpretation of the data. |

Collaborator Contribution | Provide complementary knowledge and contributed computer time. |

Impact | Development of a state of the art code, publications of high-impact articles, applications for further funding. |

Start Year | 2007 |

Description | Lattice BSM |

Organisation | University of Edinburgh |

Department | School of Physics and Astronomy |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | Code development and analysis of the results. |

Collaborator Contribution | Participation to data acquisition. |

Impact | Various research papers (most of which are listed already under the output section). |

Start Year | 2006 |

Title | BSMBench |

Description | Advanced supercomputer benchmarking software derived from research code. |

IP Reference | |

Protection | Copyrighted (e.g. software) |

Year Protection Granted | 2012 |

Licensed | Commercial In Confidence |

Impact | The software has been used by IBM to inform the final stages of design of the software stack on their BlueGene/Q, which currently is one of the most popular supercomputers. |

Title | Benchmarking |

Description | Derived from the research supercomputer code we have written, we have developed BSMBench, an advanced benchmarking technology that can be used by supercomputer vendors, users and data centre to assess the performance of the system. |

Type Of Technology | Software |

Year Produced | 2012 |

Impact | The software is currently commercialised by a spin-out company, with customers outside academia. |

Company Name | BSMBench Ltd |

Description | The business of the company is commercialisation of BSMBench and general consultancy on supercomputers. |

Year Established | 2012 |

Impact | The company has commercial relationships with IBM, Fujitsu, Microsoft. |

Description | Masterclass |

Form Of Engagement Activity | Participation in an open day or visit at my research institution |

Part Of Official Scheme? | No |

Type Of Presentation | Workshop Facilitator |

Geographic Reach | Regional |

Primary Audience | Schools |

Results and Impact | Each year around 80-100 pupils attend the Masterclasses at Swansea University, where they are introduced to the LHC and the discovery of the Higgs and get a chance to work on data of particle collisions. There has been a noticeable increase in interest from High School pupils to study Physics at Swansea. |

Year(s) Of Engagement Activity | 2010,2011,2012,2013,2014 |

Description | Public Talk |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Primary Audience | Public/other audiences |

Results and Impact | A group of 60 adults interested in science attended the talk and a lively half an hour question session was held afterwards. Several people in the audience approached me informally and asked further details about my research. |

Year(s) Of Engagement Activity | 2008 |