David Ridout's Homepage

This is my webpage. I'm a mathematical physicist, meaning that I study the mathematical structures that underlie my favourite physical theories. These include vertex operator algebras / conformal field theories and their relation with string theory, integrable models, and anything else that I can think of. At the moment, this means logarithmic conformal field theory, string theory on Lie supergroups, Temperley-Lieb representations (and its generalisations), and the integrability of non-linear sigma models. I'm especially interested in the appearance of indecomposable (but reducible) representations in physics, but pretty much anything that involves cool math is fine with me.

Currently, I'm studying examples of conformal field theories in which the correlation functions exhibit logarithmic singularities. In representation-theoretic terms, these logarithmic theories are built from representations which are indecomposable but not irreducible. Such theories arise naturally when considering so-called non-local observables (crossing probabilities, fractal dimensions) in the conformal limit of many exactly solvable lattice models (percolation, Ising). They are also relevant to string-theoretic considerations, especially when the target space admits fermionic directions, AdS/CFT, and perhaps even to black hole holography. In mathematics, there is a tantalising suggestion that logarithmic conformal field theory and Schramm-Loewner Evolution may be equivalent in some sense.

My current research aims to further our knowledge of the algebraic structures underpinning logarithmic conformal field theories. Expected outcomes include an improved understanding of the applications to statistical physics and string theory, as well as developing beautiful connections with pure mathematics.

Here you can find:

If you wish/need to contact me, you can send me an email at

david [dot] ridout [at] unimelb [dot] edu [dot] au

or come visit me at the

School of Mathematics and Statistics,
The University of Melbourne,
Parkville, Victoria, Australia, 3010.
Office: Peter Hall (Bld. 160), Rm. 159.
Phone: (+61) 3 8344 5534, Fax: (+61) 3 8344 4599.

Collections

  1. A Gainutdinov, D Ridout and I Runkel (Eds). Logarithmic Conformal Field Theory, a special issue of the Journal of Physics, A46:490301, 2013. Preface (5 pages).


Publications

  1. D Ridout, J Snadden and S Wood. An Admissible Level osp(1|2)-Model: Modular Transformations and the Verlinde Formula. 2017, arXiv:1705.04006 [hep-th] (40 pages).

  2. J Auger, T Creutzig and D Ridout. Modularity of Logarithmic Parafermion Vertex Algebras. 2017, arXiv:1704.05168 [math.QA] (28 pages).

  3. T Creutzig, S Kanade, A Linshaw and D Ridout. Schur-Weyl Duality for Heisenberg Cosets. 2016, arXiv:1611.00305 [math.QA] (41 pages).

  4. O Blondeau-Fournier, P Mathieu, D Ridout and S Wood. Superconformal Minimal Models and Admissible Jack Polynomials. Advances in Mathematics, 314:71-123, 2017, arXiv:1606.04187 [hep-th] (32 pages).

  5. O Blondeau-Fournier, P Mathieu, D Ridout and S Wood. The Super-Virasoro Singular Vectors and Jack Superpolynomials Relationship Revisited. Nuclear Physics, B913:34-63, 2016, arXiv:1605.08621 [math-ph].

  6. J Belletête, D Ridout and Y Saint-Aubin. Restriction and Induction of Indecomposable Modules over the Temperley-Lieb Algebras. 2016, arXiv:1605.05159 [math-ph] (51 pages).

  7. M Canagasabey and D Ridout. Fusion Rules for the Logarithmic N=1 Superconformal Minimal Models II: including the Ramond Sector. Nuclear Physics, B905:132-187, 2016, arXiv:1512.05837 [hep-th].

  8. M Canagasabey, J Rasmussen and D Ridout. Fusion Rules for the Logarithmic N=1 Superconformal Minimal Models I: the Neveu-Schwarz Sector. Journal of Physics, A48:415402, 2015, arXiv:1504.03155 [hep-th] (49 pages).

  9. A Morin-Duchesne, J Rasmussen and D Ridout. Boundary Algebras and Kac Modules for Logarithmic Minimal Models. Nuclear Physics, B899:677-769, 2015, arXiv:1503.07584 [hep-th].

  10. D Ridout and S Wood. Relaxed Singular Vectors, Jack Symmetric Functions and Fractional Level sl(2) Models. Nuclear Physics, B894:621-664, 2015, arXiv:1501.07318 [hep-th].

  11. D Ridout and S Wood. From Jack Polynomials to Minimal Model Spectra. Journal of Physics, A48:045201, 2015, arXiv:1409.4847 [hep-th] (17 pages).

  12. D Ridout and S Wood. The Verlinde Formula in Logarithmic CFT. Journal of Physics: Conference Series, 597:012065, 2015, arXiv:1409.0670 [hep-th] (11 pages).

  13. D Ridout and S Wood. Bosonic Ghosts at c=2 as a Logarithmic CFT. Letters in Mathematical Physics, 105:279-307, 2015, arXiv:1408.4185 [hep-th].

  14. D Ridout and S Wood. Modular Transformations and Verlinde Formulae for Logarithmic (p_+,p_-)-Models. Nuclear Physics, B880:175-202, 2014, arXiv:1310.6479 [hep-th].

  15. T Creutzig and D Ridout. Modular Data and Verlinde Formulae for Fractional Level WZW Models II. Nuclear Physics, B875:423-458, 2013, arXiv:1306.4388 [hep-th].

  16. T Creutzig, D Ridout and S Wood. Coset Constructions of Logarithmic (1,p)-Models. Letters in Mathematical Physics, 104:553-583, 2014, arXiv:1305.2665 [math.QA].

  17. T Creutzig and D Ridout. Logarithmic Conformal Field Theory: Beyond an Introduction. Journal of Physics, A46:494006, 2013, arXiv:1303.0847 [hep-th] (72 pages).

  18. A Babichenko and D Ridout. Takiff Superalgebras and Conformal Field Theory. Journal of Physics, A46:125204, 2013, arXiv:1210.7094 [math-ph] (26 pages).

  19. T Creutzig and D Ridout. Modular Data and Verlinde Formulae for Fractional Level WZW Models I. Nuclear Physics, B865:83-114, 2012, arXiv:1205.6513 [hep-th].

  20. D Ridout and Y Saint-Aubin. Standard Modules, Induction and the Temperley-Lieb Algebra. Advances in Theoretical and Mathematical Physics, 18:957-1041, 2014, arXiv:1204.4505 [math-ph].

  21. D Ridout. Non-Chiral Logarithmic Couplings for the Virasoro Algebra. Journal of Physics, A45:255203, 2012, arXiv:1203.3247 [hep-th] (12 pages).

  22. T Creutzig and D Ridout. W-Algebras Extending gl(1|1). Springer Proceedings in Mathematics and Statistics, 36:349--368, 2013, arXiv:1111.5049 [hep-th].

  23. T Creutzig and D Ridout. Relating the Archetypes of Logarithmic Conformal Field Theory. Nuclear Physics, B872:348-391, 2013, arXiv:1107.2135 [hep-th].

  24. D Ridout and J Teschner. Integrability of a Family of Quantum Field Theories Related to Sigma Models. Nuclear Physics, B853:327-378, 2011, arXiv:1102.5716 [hep-th].

  25. D Ridout. Fusion in Fractional Level sl(2)-Theories with k=-1/2. Nuclear Physics, B848:216-250, 2011, arXiv:1012.2905 [hep-th].

  26. D Ridout. sl(2)_{-1/2} and the Triplet Model. Nuclear Physics, B835:314-342, 2010, arXiv:1001.3960 [hep-th].

  27. K Kytölä and D Ridout. On Staggered Indecomposable Virasoro Modules. Journal of Mathematical Physics, 50:123503, 2009, arXiv:0905.0108 [math-ph] (51 pages).

  28. D Ridout. sl(2)_{-1/2}: A Case Study. Nuclear Physics, B814:485-521, 2009, arXiv:0810.3532 [hep-th].

  29. D Ridout. On the Percolation BCFT and the Crossing Probability of Watts. Nuclear Physics, B810:503-526, 2009, arXiv:0808.3530 [hep-th].

  30. P Mathieu and D Ridout. Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality. Nuclear Physics, B801:268-295, 2008, arXiv:0711.3541 [hep-th].

  31. P Mathieu and D Ridout. From Percolation to Logarithmic Conformal Field Theory. Physics Letters, B657:120-129, 2007, arXiv:0708.0802 [hep-th].

  32. P Mathieu and D Ridout. The Extended Algebra of the Minimal Models. Nuclear Physics, B776:365-404, 2007, arXiv:hep-th/0701250 .

  33. P Mathieu and D Ridout. The Extended Algebra of the SU(2) Wess-Zumino-Witten Models. Nuclear Physics, B765:201-239, 2007, arXiv:hep-th/0609226 .

  34. P Bouwknegt and D Ridout. Presentations of Wess-Zumino-Witten Fusion Rings. Reviews in Mathematical Physics, 18:201-232, 2006, arXiv:hep-th/0602057 .

  35. P Bouwknegt and D Ridout. A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models. Journal of High Energy Physics, 05(2004)029, arXiv:hep-th/0312259 (13 pages).

  36. P Bouwknegt, P Dawson, and D Ridout. D-Branes on Group Manifolds and Fusion Rings. Journal of High Energy Physics, 12(2002)065, arXiv:hep-th/0210302 (22 pages).

  37. D Ridout and K Judd. Convergence Properties of Gradient Descent Noise Reduction. Physica, D165:26-47, 2002.

  38. P Bouwknegt, L Chim, and D Ridout. Exclusion Statistics in Conformal Field Theory and the UCPF for WZW models. Nuclear Physics, B572:547-573, 2000, arXiv:hepth/9903176.


Seminar Slides and Posters


Theses


Supervision


Personal Information

I'm an Australian, a sandgroper from Perth. You can tell this by my impeccable spelling. I graduated from Rossmoyne Senior High School before starting a BSc at Murdoch University. A few years later, I found myself burdened with a double degree in mathematics and physics (and 3/4 of a degree in chemistry). Embracing the financial poverty that was now my destiny, I completed an honours degree in operator theory and three-body quantum scattering. I then moved on to the University of Western Australia (who will no doubt complain that I haven't capitalised the "T" in "the") where I occupied myself with a masters degree in the theory of topological chaotic dynamics and its application to noise reduction algorithms.

I then moved to Adelaide to start a PhD at the University of Adelaide. There, I was introduced to the wonderful world of conformal field theory and tried in vain to pick up the rudiments of string theory. With a little Lie theory, algebraic topology, differential geometry, and commutative algebra, I wrote a thesis on D-brane charges and fusion rings in Wess-Zumino-Witten models. The last two years of my doctoral studies were completed as a guest of the maths department at La Trobe University in Melbourne; without their generosity, things would have been rather difficult.

I then moved to Québec as a postdoc with Pierre Mathieu. There, I worked on extending the chiral algebras of various conformal field theories and made some forays into the world of logarithmic conformal field theory. I also managed to find time to try a bit of skiing and skating, though the intricate art of curling remained elusive. As did a solid grasp of the french language, or at least the local dialect.

Then, I moved to the DESY Theory Group in Hamburg with Jörg Teschner. There, I continued my romping in logarithmic conformal fields and also branched out into the wider world of deformed conformal field theories, integrable models and quantum groups. I tried once again to learn some basic string theory, but it seems that my brain is set on rejecting all such knowledge transplants. Luckily, I had ample opportunity to sample the joys of living in continental Europe, with its myriad of confusing cultures and its myriad of confusing languages. I will miss the cheese most of all...

Well, I ended up back in Canada, this time in Montréal, with Yvan Saint-Aubin, doing mathematics once again. I also had the luck to get some lecturing in the McGill University maths department while I worked on my French. It certainly wasn't hard to recreate the joy of living in that beautiful country, while simultaneously working very hard on new and interesting problems. And getting fat on the ubiquitous (and cheap!) french patisseries! Plus, Montréal has lots of cheese, lovely lovely cheese (and I don't count that horrible poutine cheese either!).

As luck would have it, my time in Montréal was cut short by a not-to-be-refused grant application unexpectedly getting funded. I returned to Australia as an Australian Research Fellow at the Australian National University in Canberra. There, I got to wallow in the muddy waters of logarithmic conformal field theories and teach myself some vertex algebra theory for five whole years. Happy times, though I was horrified at how expensive Australia had become. Even the local cheeses exceeded expectations hugely (mmm, Small Cow Farm's Redella).

This saga has a happy ending. The clever sods in the School of Mathematics and Statistics at the University of Melbourne decided to take pity on me and give me a continuing position. This was a dangerous gambit given the University's close proximity to the cheesemongers of the Queen Vic Markets, but so far everyone seems to be happy. Especially me. All I need to do now is a bit of work (and not to think about property prices). Wish me luck! I promise to return the favour someday...