I am a high-energy particle theorist whose wild oats were sown working in string theory, but my research interests have since taken a more phenomenological and cosmological turn. At present my interests lie at the interface between string theory and lower-energy physics, with a particular emphasis on how the discovery of D-branes (and the realization that we may be trapped on one) may have observable consequences in experiments and in cosmology. I have also been a tourist in some of those fields which are related to my own, and am interested in most of the cool applications of theoretical physics.

To the extent that there is a theme to my research, it would be the use of effective field theory techniques throughout high-energy physics and other fields. These techniques permit a general understanding of the low-energy (or long-wavelength) behaviour of any physical system. They are particularly apt for our present situation in particle physics, where it appears that the energy scale of any unknown physics beyond the Standard Model is high compared to those that are experimentally accessible. But part of the beauty of these techniques is that they are also applicable in other areas of physics and so they permit a unified perspective towards theoretical physics as a whole.

Here is a selection of three recent areas that lie particularly close to my research heart:

- Dark Energy and Supersymmetric Large Extra Dimensions;
- String Inflation
- Quantum Hall Systems and ADS/CFT Duality

#### EXTRA DIMENSIONS AND DARK ENERGY

In recent years cosmologists were able to survey the energy content of the universe, with surprising results. Because their survey relies on how things gravitate, rather than on whether they are directly visible, it includes even those things that are intrinsically “dark”. The surprise is that 95% of the universe’s energy density appears to be made of two different kinds of unknown forms of stuff: Dark Matter (about 25% of the total energy density) and Dark Energy (about 70% of the total).

Although neither of these is really understood at present, Dark Energy seems the more difficult of the two to fit into what we know. This is because although Dark Energy is very plausibly interpretable as the energy density of the vacuum itself, it is measured to be incredibly small compared with the energy density we believe we can calculate the vacuum to have. For instance, quantum fluctuations of the electron – perhaps the best-understood particle we have – alone contributes 10^{36} times too much vacuum energy compared with what is observed.

The following articles describe a proposal which I believe provides the best approach to date towards understanding the nature of the Dark Energy density. In essence they argue that the mismatch between the calculated and observed sizes to the vacuum energy can be resolved if there are two extra dimensions that are as large as they can possibly be without having been already detected (ie around 1-10 microns across). In this picture the vacuum energy mostly curves the extra dimensions, with only a small portion contributing to what is measured in cosmology.

If this is the way Nature works it will be hard to miss. It predicts: Newton’s law of gravity changes from inverse-square to inverse fourth-power at distances around 1-10 microns; the LHC should see quantum gravity, which most likely means excited string versions of all of the known ordinary particles with masses lower than around 10 TeV; gravity on astrophysical and cosmological distances is modified by a very long-range scalar force (whose small mass is also understood in a natural way), among other things.

The main proposal is given in the following papers

1) **Towards a Naturally Small Cosmological Constant from Branes in 6D Supergravity**, Y. Aghababaie, C.P. Burgess, S. Parameswaran and F. Quevedo, Nuclear Physics B680 (2004) 389-414, (hep-th/0304256);

2) **Technically Natural Cosmological Constant From Supersymmetric 6D Brane Backreaction**, C.P. Burgess and Leo van Nierop (arXiv:1108.0345);

which rely on the properties of gauged six-dimensional supergravity (and how it responds to the presence of brane sources), as outlined in these papers

3) **Warped Brane Worlds in Six Dimensional Supergravity**, Y. Aghababie, C.P. Burgess, J.M. Cline, H. Firouzjahi, F. Quevedo, G. Tasinato and I. Zavala, Journal of High Energy Physics 0309 (2003) 037 (hep-th/0308064);

4) **General Axisymmetric Solutions and Self-Tuning in 6D Chiral Gauged Supergravity**, C.P. Burgess, F. Quevedo, G. Tasinato and I. Zavala, Journal of High-Energy Physics 0411 (2004) 069 (hep-th/0408109);

5) **Large Dimensions and Small Curvatures from Supersymmetric Brane Back-reaction**, C.P. Burgess and L. van Nierop, JHEP 1104 (2011) 078 (arXiv:1101.0152);

6) **Bulk Axions, Brane Back-reaction and Fluxes**, C.P. Burgess and L. van Nierop, JHEP 1102 (2011) 094 (arXiv:1012.2638).

More recent reviews of this proposal, and how it works are in:

7) **The Cosmological Constant Problem: Why it is Hard to get Dark Energy from Micro-Physics**, C.P. Burgess, in the proceedings of the Les Houches summer school Post-Planck Cosmology, Les Houches France, July 2013, (arXiv:1308.xxxx);

8) **Extra Dimensions and the Cosmological Constant Problem**, C.P. Burgess, in the proceedings of Rencontres de Moriond 2007, Electroweak and Unified Theories, La Thuile, Italy, March 2007, (arXiv:0708.0911);

9) **Towards a Natural Theory of Dark Energy: Supersymmetric Large Extra Dimensions**, C.P. Burgess, in the proceedings of Strings and Cosmology, Texas A&M University, College Station Texas, March 2004, AIP Conference Proceedings 743 (2005) 417-449, (hep-th/0411140);

10) **Supersymmetric Large Extra Dimensions and the Cosmological Constant: An Update**, C.P. Burgess, Annals of Physics 313/2 (2004) 383—401 (hep-th/0402200);

Issues to do with the sensitivity of the Dark Energy to renormalization effects (the traditional cosmological constant problem) are explored in:

11) **Technical Naturalness on a Codimension-2 Brane**, C.P. Burgess, D. Hoover and G. Tasinato, (arXiv:0903.0402);

12) **Effective Field Theories and Matching for Codimension-2 Branes**, C.P. Burgess, C. de Rham, D. Hoover and G. Tasinato, (arXiv:0812.3820);

13) **UV Caps and Modulus Stabilization for 6D Gauged Chiral Supergravity**, C.P. Burgess, D. Hoover and G. Tasinato, (arXiv:0705.3212);

14) **Ultraviolet Sensitivity in Supersymmetric Large Extra Dimensions: The Ricci-Flat Case**, Journal of High Energy Physics, C.P. Burgess and D. Hoover, (hep-th/0504004);

15) **Ultraviolet Sensitivity in Higher Dimensions**, D. Hoover and C.P. Burgess, Journal of High Energy Physics 0601 (2006) 058 (hep-th/0507293);

Issues to do with the sensitivity of the resulting Dark Energy to initial conditions are explored in:

16) **Scaling Solutions to 6D Gauged Chiral Supergravity**, A.J. Tolley, C.P. Burgess, C. de Rham and D. Hoover, New Journal of Physics 8 (2008) 324, (hep-th/0608083);

17) **Kicking the Rugby Ball: Perturbations to 6D Gauged Chiral Supergravity**, C.P. Burgess, C. de Rham, D. Hoover, D. Mason and A.J. Tolley, Journal of Cosmology and Particle Physics 0702 (2007) 009 (hep-th/0610078);

Best of all, this proposal has a number of striking observational consequences, some of which are explored in:

18) **Natural Quintessence and Large Extra Dimensions**, A. Albrecht, C.P. Burgess, F. Ravndal and C. Skordis, Physical Review D65 (2002) 123507 (astro-ph/0107573);

19) **MSLED: A Minimal Supersymmetric Large Extra Dimensions Scenario**, C.P. Burgess, J. Matias and F. Quevedo, Nuclear Physics B706 (2005) 71-99 (hep-ph/0404135);

20) **Deviations from Newton’s Law in Supersymmetric Large Extra Dimension**s, P. Callin and C.P. Burgess, Nuclear Physics B (to appear) (hep-th/0511216);

21) **MSLED, Neutrino Oscillations and the Cosmological Constant**, J. Matias and C.P. Burgess, Journal of High Energy Physics 0509 (2005) 052 (hep-ph/0508156);

22) **Dimensionless Coupling of Bulk Scalars at the LHC**, P.-H. Beauchemin, G. Azuelos and C.P. Burgess, Journal of Physics G30 (2004) N17 (15 pages) (hep-ph/0407196);

23) **Phenomenological Constraints on Extra-Dimensional Scalars**, G. Azuelos, P.-H. Beauchemin and C.P. Burgess, Journal of Physics G31 (2005) 1-19, (hep-ph/0401125);

#### STRING INFLATION

I have also been involved in recent attempts to embed cosmic inflation into string theory. The motivation here comes from precision measurements of the cosmic microwave background radiation, which is a residue of a much-earlier time when the universe was smaller and hotter. These observations find evidence for a pattern of density fluctuations in the primordial distribution of matter in the very early universe.

The observed pattern (so far) fits well with what would be expected if the very-early universe underwent a period of accelerated expansion, called cosmic inflation, during which it grew enormously. But because the universe was then so small and hot, it was described by physical laws which we cannot yet probe directly in experiments on earth, and so nobody knows for sure how this kind of inflation could have arisen. Because string theory provides our best understanding of gravity under extreme circumstances, it also provides our best bet (so far) for the physics that should describe such early events.

In a nutshell, inflation and string theory could be made for each other: string theory might provide an explanation for why the universe inflated, and inflation might provide the first observational tests of string theory. This has motivated a detailed search for whether and how inflation might arise within string theory.

An overview of some of these attempts may be found in the review (in view of recent data):

1) **String Inflation after Planck 2013,** C.P. Burgess, M. Cicoli and F. Quevedo, (arXiv:1306.3512);

and the lectures:

2) **Lectures on Cosmic Inflation, and its Possible Stringy Realizations**, C.P. Burgess, given to schools in Dubrovnik (Aug 2006); CERN (January 2007) and Cargese (August 2007), (arXiv:0708.2865);

I was involved with proposing some of the main inflationary mechanisms which have been identified in string theory to this point, such as

Brane-Antibrane Inflation:

3) **The Inflationary brane anti-brane universe**, C.P. Burgess, M. Majumdar, D. Nolte, F. Quevedo, G. Rajesh and R.-J. Zhang , Journal of High Energy Physics 0107 (2001) 047, (hep-th/0105204);

4) **Inflation in Realistic D-Brane Models**, C.P. Burgess, J.M. Cline, H. Stoica and F. Quevedo, Journal of High Energy Physics 0409 (2004) 033 (hep-th/0403119);

Inflation due to Shape-Change in the Extra Dimensions:

5) **Fibre Inflation: Observable Gravity Waves from Type IIB String Compactifications**, M. Cicoli, C.P. Burgess and F. Quevedo, Journal of Cosmology and Astro-Particle Physics 0903 (2009) 013 (arXiv:0808.0691);

6) **Brane-Antibrane Inflation in Orbifold and Orientifold Models**, C.P. Burgess, P. Martineau, F. Quevedo, G. Rajesh and R.-J. Zhang, Journal of High Energy Physics 0203 (2002) 052 (hep-th/0111025);

7) **Racetrack Inflation**, J.J. Blanco-Pillado, C.P. Burgess, J.M. Cline, C. Escoda, M. Gomez-Reino, R. Kallosh, A. Linde and F. Quevedo, Journal of High Energy Physics 0411 (2004) 069 (hep-th/0406230);

8) **Inflating in the Better Racetrack**, J.J. Blanco-Pillado, C.P. Burgess, J.M. Cline, C. Escoda, M. Gomez-Reino, R. Kallosh, A. Linde and F. Quevedo, (hep-th/06003129);

String realizations of non-standard mechanisms for generating primordial fluctuations, with potentially observable implications for the non-Gaussianity of the cosmic microwave background radiation:

9) **Non-standard primordial fluctuations and nongaussianity in string inflation**, C.P. Burgess, M. Cicoli, M. Gomez-Reino, F. Quevedo, G. Tasinato and I. Zavala, JHEP 1008 (2010) 045 (arXiv:1005.4840);

10) **Modulated Reheating and Large Non-Gaussianity in String Cosmology**, M. Cicoli, G. Tasinato, I. Zavala, C.P. Burgess and F. Quevedo, (arXiv:1202.4580).

#### DUALITY, THE ADS/CFT CORRESPONDENCE AND THE QUANTUM HALL EFFECT

Quantum Hall systems involve electrons confined to live at the two-dimensional interface between two kinds of semi-conductors, in the presence of a large magnetic field. When examined at very low temperatures in very clean samples, electrons in this kind of environment display a variety of exotic and remarkable quantum properties.

Although the fundamental understanding of what the electrons are doing was achieved in the 1980s, through the work of Laughlin and others, some aspects of these systems have remained puzzling. In particular, one of the puzzles is the remarkable robustness of a suite of experimental features these systems share as one changes the strength of the magnetic field at low temperatures. This robustness suggests there should be an emergent low-energy description that does not depend on the electrons’ microscopic details.

The following articles describe how I believe emergent symmetries (initially proposed by Lutken & Ross and Kivelson, Lee and Zhang) provide a crucial clue for how to understand the robustness of the low-energy features of quantum Hall systems.

These papers argue that the duality symmetries would provide a robust explanation for the suite of experimental observations that characterize the low-temperature transitions between quantum Hall plateaux. For ordinary quantum Hall systems these include the observed “semi-circle law” and duality observations that go beyond the linear response approximation, although several implications for novel quantum Hall features of bilayer systems and graphene are also explored

1) **Derivation of the semicircle law from the law of corresponding states**, C.P. Burgess, Rim Dib and Brian P. Dolan,

Phys.Rev. B62 (2000) 15359-15362 (cond-mat/9911476);

2) **Duality and nonlinear response for quantum Hall systems**,

C.P. Burgess and Brian P. Dolan, Phys.Rev. B65 (2002) 155323

(cond-mat/0105621);

3) **Duality, the Semi-Circle Law and Quantum Hall Bilayers**,

C.P. Burgess and B.P. Dolan, Phys.Rev. B76 (2007) 155310

(cond-mat/0701535);

4) **The Quantum Hall effect in graphene: Emergent modular symmetry and the semi-circle law**, C.P. Burgess and Brian P. Dolan, Phys.Rev. B76 (2007) 113406 (cond-mat/0612269);

This paper argues that the required duality symmetries could arise from particle-vortex duality, and predicts a new class of observational tests for quantum Hall systems built from bosonic charge carriers

3) **Particle vortex duality and the modular group: Applications to the quantum Hall effect and other 2-D systems**, C.P. Burgess and Brian P. Dolan, Phys.Rev. B63 (2001) 155309 (hep-th/0010246);

These papers argue that the ADS/CFT correspondence provide a very natural framework for describing the conformal field theories (CFTs) that control quantum Hall systems in the far infrared

4) **AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments**, Allan Bayntun, C.P. Burgess, Brian P. Dolan and Sung-Sik Lee, New J.Phys. 13 (2011) 035012 (arXiv:1008.1917);

5) **Finite Size Scaling in Quantum Hallography**, Allan Bayntun and C.P. Burgess (arXiv:1112.3698)