String theory is wonderful! It can explain everything!! In principle it can explain why there are four space-time dimensions, why gravitation is described by general relativity, why strong interactions are described by quantum chromodynamics, and electroweak interactions by the Glashow-Weinberg-Salam gauge theory; it can explain why there are leptons and quarks, why there are three generations of them; explain the strength of all interactions and the masses of all particles, and predict low-energy supersymmetry and its (soft) breaking.

However, in practice there is still a way to go, since non-perturbative effects are poorly understood. My work on string theory has been primarily devoted to the "orbifold compactifications" of (weakly-coupled heterotic) string theory. In its simplest form the quantum consistency of superstring theory requires the existence of ten space-time dimensions. The unobserved six spatial dimensions are compactified on an orbifold, which is defined as a torus on which points related by the action of a discrete "point group" have been identified. The orbifold is then flat everywhere except for a finite number of "fixed points", where there are conical singularities.

With collaborators I have  been concerned with the stringy "target space" symmetries of the orbifold "moduli". These are the scale factors (radii) and complex structures which characterise the compact space formed by the extra spatial dimensions required by string theory. The effective interaction strengths vary ("run") with the energy scale at which they are measured, and their variation is determined by the whole spectrum of particles in the theory. Starting from their values measured in laboratories, at energy scales of order m_z, the three different couplings are calculated to evolve to a unified value at an energy scale of 2x10¹⁶GeV, provided we assume that all known particles have supersymmetric partners, the so-called (minimal) Supersymmetric Standard Model. However string theory requires that all coupling strengths have the same value at the string scale of 4x10¹⁷GeV.

This may mean that string theory is wrong(!), but a preferred explanation is that threshold corrections to the interaction strengths, deriving from massive string loop effects, may explain the discrepancy. These threshold corrections depend upon the moduli, and their symmetries also characterise the non-perturbative superpotential, which in turn fixes the effective potential whose minimum controls the actual values of the moduli observed in nature. The moduli also affect the soft supersymmetry breaking terms, as well as the masses and mixing angles of the quarks and leptons. They can induce CP-violation and hence an electric dipole moment for the neutron and the electron, both currently the subject of experimental research by Sussex groups. The overall aim is to obtain a consistent understanding of all of these related effects.

Other possibilities that have been explored in recent work are  that the heterotic string is strongly coupled, or that other (Type I/II) superstring theories are relevant. In the former case the original ten-dimensional weakly-coupled theory is now recognised as a limiting case of ''heterotic M-theory'', an eleven-dimensional theory with two nine spatial dimensional spaces separated by a spatial interval in the eleventh dimension. Gravitaional fields propagate in all eleven (space-time) dimensions, but the gauge interactions and matter fields which we encounter are  confined to one of the two ten-dimensional spacetimes at the ``end'' of the universe. This theory can explain the discrepancy between the ''observed'' unification scale and the string scale by choosing the length of the interval separating the two nine-dimensional spaces appropriately. The theory also admits the possibility of five (spatial) dimensional spaces (5-branes) situated at intermediate points on the interval between the nine-dimensional spaces, and all of these have moduli that can affect the soft supersymmetry breaking terms and hence the sparticle spectrum and dark matter abundances.

The second possible resolution of the discrepancy also utilises  higher-dimensional objects (p-branes) besides (1-branes) strings. The existence of Dirichlet p-branes  on which open strings may end has afforded totally new possiblities in string theory in which a bottom-up approach may be used to construct consistent theories that have gauge group and matter content very close to that of the standard model. In recent years, using four stacks of D6-branes wrapping 3-cycles of a Z6'-orientifold, we have constructed models with the spectrum of the supersymmetric Standard Model (plus three right-chiral neutrinos).

Selected Publications

• Introduction to Gauge Field Theory, Revised Edition, IOP Publishing, 1993

• Supersymmetric gauge field theory and string theory, IOP Publishing, 1994.

• Cosmology in Gauge Field Theory and String Theory , IOP Publishing, 2004.

• The supersymmetric CP problem in orbifold compactifications, Nuclear Physics B, 512, 92-116, 1998.

• Cosmological inflation with orbifold moduli as inflatons Physics Letters B 443 (1998)111-120 (with G. V. Kraniotis and A. Love)

• Orbifold compactifications of string theory, Physics Reports, 315, 285-408, 1999,

•  Non-minimal Higgs content in standard-like models from D-branes at a Z_N singularity , Physics Letters B 598 (2004) 83-91 (with A. Love).

•  Towards the supersymmetric Standard Model from intersecting D6-branes on the Z_6' orientifold , Nuclear Physics B 755 (2006) 79-111 (with A. Love).

• Constructing the supersymmetric Standard Model from intersecting D6-branes on the Z_6' orientifold, Nuclear Physics B809 (2009) 64-109 (with A. Love).

• Stabilising the supersymmetric Standard Model on the Z_6' orientifold, Nuclear Physics B854 (2012) 700-737 (with A. Love).

Popular Articles

• The structure of the vacuum, Sciences et Avenir No. 112 (1997) 86-89

• Electroweak unification, Sciences et Avenir No. 118 (1999) 54-59

• Review of "The Elegant Universe" by Brian Greene, (Jonathan Cape, 1999) New Scientist June 12th, 1999, p44

Talks

• CP violation in string theory, Durham colloquium, March 1, 2001

• Supersymmetric Standard Model on D-branes, Oxford, February 9, 2001

• Standard model on D-branes, India, January & February, 2002

• Strings, Branes and the Universe Unravelled, Edinburgh Science Festival, April 18, 2003.

• The Nobel Prize in Physics 2004, Sussex, October 27, 2004.

•  Why do we exclude field theories having particles with helicity >2?  Sussex Particle Theory talk, 2005.

• Constructing the supersymmetric standard model from the Z_6' orientifold, String Phenomenology & Vacuum Selection, Liverpool, March 27, 2008.