# New Ideas in Gauge, String and Lattice Theory

Lead Research Organisation:
University of Plymouth

Department Name: Sch of Computing, Electronics & Maths

### Abstract

The standard model of particle physics encodes our current knowledge of the fundamental constituents of atoms and the nature of matter in the earliest moments following the Big Bang. However, our understanding of the dynamics of the standard model is limited by our ability to solve its strongly-interacting sector, quantum chromodynamics (QCD), which describes the interactions of quarks and gluons. The Swansea and Plymouth groups are approaching this problem from two complementary perspectives. By approximating the continuum of spacetime as a discrete lattice of points, it is possible to simulate QCD on high performance computers. The groups will study lattice QCD in the extreme conditions of high temperature and density which existed following the Big Bang and which can now be realised in heavy-ion collisions at the Large Hadron Collider (LHC) at CERN. These investigations will be complemented by analytic insights arising from `gauge-gravity duality', a remarkable principle which relates the theories describing particle physics with properties of general relativity.

The primary goal of the LHC is, however, to discover the new physics which is responsible for the generation of mass for the elementary particles. This `electroweak symmetry breaking' is the least understood part of the standard model. It may be due to the existence of a background field permeating spacetime, which gives mass to particles as they interact with it. On the other hand, mass generation may be due to the existence of a new strong interaction at the TeV energy scale

probed by the LHC. In both cases, the theories predict the existence of a new spin zero particle, the famous Higgs boson recently discovered at the LHC. Distinguishing these possibilities is a subtle problem and once again we are attempting to resolve the question using both gauge-gravity duality and lattice simulations.

Particle physicists do not, however, believe that the standard model is the ultimate theory of nature. It is an example of a gauge theory, a theoretical framework which unifies quantum mechanics and special relativity together with the fundamental symmetries which physicists have discovered through decades of experiments with particle accelerators. Meanwhile, gravity remains outside this framework, being described by general relativity in terms of the curvature of spacetime. A deeper unification appears possible with superstrings, which contain both gauge theories and gravity together with a new type of spacetime symmetry known as supersymmetry. The Swansea group is therefore complementing its investigations of LHC physics with research into the deeper structure of gauge fields and strings, using fundamental ideas such as gauge-gravity duality and `quantum integrability' in the search for the underlying principles behind our current theories of particle physics.

The primary goal of the LHC is, however, to discover the new physics which is responsible for the generation of mass for the elementary particles. This `electroweak symmetry breaking' is the least understood part of the standard model. It may be due to the existence of a background field permeating spacetime, which gives mass to particles as they interact with it. On the other hand, mass generation may be due to the existence of a new strong interaction at the TeV energy scale

probed by the LHC. In both cases, the theories predict the existence of a new spin zero particle, the famous Higgs boson recently discovered at the LHC. Distinguishing these possibilities is a subtle problem and once again we are attempting to resolve the question using both gauge-gravity duality and lattice simulations.

Particle physicists do not, however, believe that the standard model is the ultimate theory of nature. It is an example of a gauge theory, a theoretical framework which unifies quantum mechanics and special relativity together with the fundamental symmetries which physicists have discovered through decades of experiments with particle accelerators. Meanwhile, gravity remains outside this framework, being described by general relativity in terms of the curvature of spacetime. A deeper unification appears possible with superstrings, which contain both gauge theories and gravity together with a new type of spacetime symmetry known as supersymmetry. The Swansea group is therefore complementing its investigations of LHC physics with research into the deeper structure of gauge fields and strings, using fundamental ideas such as gauge-gravity duality and `quantum integrability' in the search for the underlying principles behind our current theories of particle physics.

### Planned Impact

The Pathways to Impact document summarises the activities of the Plymouth and Swansea groups in the areas of Knowledge Exchange and Outreach.

Knowledge Exchange is centred on the exploitation of HPC facilities, especially through the close involvement of the UKQCD collaboration with IBM and the development of the Blue Gene series of supercomputers. The Swansea group has established a close contact with IBM Research at Yorktown Heights, running lattice code as a benchmark application to evaluate computer performance and development. This has led to the creation of a third-party company, BSMBench Ltd, to commercialise a benchmarking tool developed from the group's research in lattice gauge theory. Through UKQCD, both groups are active in developing Grid technology.

Outreach activities are focused in three areas - schools activities, popular lectures and media involvement. The Swansea group organises two activities for schools: Particle Physics Masterclasses for 6th form students with lectures and hands-on computer sessions using ATLAS software to analyse LHC events, and annual Christmas lectures for younger pupils. Group members give frequent public lectures and organise the local Swansea `Science Cafe'. The excitement surrounding the first experimental results and discovery of the Higgs boson at CERN, as well as the achievement of the Physics Department's atomic physics group in creating and trapping atoms of antihydrogen at CERN, have been exploited in numerous TV and radio presentations as well as in newspaper and magazine articles. The keynote lecture by Peter Higgs at the `Strong and Electroweak Matter' conference in Swansea in July 2012 was streamed to schools across the U.K. and an interview with Peter was posted on the University's website and You Tube.

Knowledge Exchange is centred on the exploitation of HPC facilities, especially through the close involvement of the UKQCD collaboration with IBM and the development of the Blue Gene series of supercomputers. The Swansea group has established a close contact with IBM Research at Yorktown Heights, running lattice code as a benchmark application to evaluate computer performance and development. This has led to the creation of a third-party company, BSMBench Ltd, to commercialise a benchmarking tool developed from the group's research in lattice gauge theory. Through UKQCD, both groups are active in developing Grid technology.

Outreach activities are focused in three areas - schools activities, popular lectures and media involvement. The Swansea group organises two activities for schools: Particle Physics Masterclasses for 6th form students with lectures and hands-on computer sessions using ATLAS software to analyse LHC events, and annual Christmas lectures for younger pupils. Group members give frequent public lectures and organise the local Swansea `Science Cafe'. The excitement surrounding the first experimental results and discovery of the Higgs boson at CERN, as well as the achievement of the Physics Department's atomic physics group in creating and trapping atoms of antihydrogen at CERN, have been exploited in numerous TV and radio presentations as well as in newspaper and magazine articles. The keynote lecture by Peter Higgs at the `Strong and Electroweak Matter' conference in Swansea in July 2012 was streamed to schools across the U.K. and an interview with Peter was posted on the University's website and You Tube.

### Publications

Pellegrini R.
(2014)

*The density of states from first principles*in arXiv e-prints
Patella A
(2014)

*Space-time symmetries and the Yang-Mills gradient flow*
Patella A
(2014)

*Space-time symmetries and the Yang-Mills gradient flow*
Lucini Biagio
(2014)

*A novel density of state method for complex action systems*in arXiv e-prints
Lucini Biagio
(2015)

*Investigating Some Technical Improvements to Glueball Calculations*in PoS
Langfeld K
(2014)

*Towards a density of states approach for dense matter systems*
Langfeld K
(2016)

*From the Density-of-states Method to Finite Density Quantum Field Theory*in Acta Physica Polonica B Proceedings Supplement
Langfeld K
(2014)

*Density of states approach to dense quantum systems*in Physical Review D
Langfeld K
(2016)

*An efficient algorithm for numerical computations of continuous densities of states*in The European Physical Journal C
Langfeld K
(2015)

*The density of states approach for the simulation of finite density quantum field theories*in Journal of Physics: Conference Series
Langfeld K
(2014)

*Towards a density of states approach for dense matter systems*
Greensite J
(2014)

*Finding the effective Polyakov line action for SU(3) gauge theories at finite chemical potential*in Physical Review D
Gliozzi F
(2014)

*Critical exponents of the 3d Ising and related models from conformal bootstrap*in Journal of High Energy Physics
Gliozzi F
(2015)

*Boundary and interface CFTs from the conformal bootstrap*in Journal of High Energy Physics
Gattringer C
(2016)

*Approaches to the sign problem in lattice field theory*in International Journal of Modern Physics A
Del Debbio Luigi
(2013)

*Large-volume results in SU(2) with adjoint fermions*
Del Debbio L
(2016)

*Large volumes and spectroscopy of walking theories*in Physical Review D
Athenodorou A
(2015)

*Infrared regime of SU(2) with one adjoint Dirac flavor*in Physical Review DDescription | Central to this award have been the developments of a new first principle numerical method to address the properties of dense matter in quantum field theories and, most notably, QCD - the theory of strong interactions. For more than three decades, the notorious sign problem prevented computer simulations to provide exact results (within controllable error margins). Here, we succeeded to generalise the density-of-states approach in the LLR formulation (developed by us Phys.Rev.Lett. 109 (2012) 111601) to finite density quantum field theories: using the Z3 theory (for which results are available by means of a suitable reformulation) as a proof of concept, we demonstrated that the sign-problem can be resolved with the LLR approach. Work is in progress and has reached the publication stage for QCD at finite density for heavy quarks (HDQCD). We also put the LLR method on firm grounds by a through study of its convergence and ergodicity properties (see ref "An efficient algorithm for numerical computations of continuous densities of states" of this award). |

Exploitation Route | Our approach is now in the process to be taken up by other research groups. |

Sectors | Digital/Communication/Information Technologies (including Software),Education,Financial Services, and Management Consultancy,Other |