T H O M A S   C R E U T Z I G   



thomas
Associate Professor
University of Alberta
Department of Mathematical and Statistical Sciences
Edmonton, AB T6G 2G1

Office location: 573 CAB
Office phone: + 1 780 492 5737
email: lastname at ualberta dot ca




R E S E A R C H

My research is in mathematical physics around two-dimensional conformal field theories, vertex operator algebras and their various exciting applications. These range from string theory, quantum gravity and quantum field theory to topology, geometry, number theory, tensor categories and representation theory. The current exciting development are 2d/4d correspondences where representation theory of the chiral algebras, that is the vertex operator algebras, of two-dimensional conformal field theories appear as rich invariants of four-dimensional super Yang-Mills theories.

Conferences



P U B L I C A T I O N S


Preprints of publications are on the arXiv


P H Y S I C S

[1.] T. Creutzig, T. Quella and V. Schomerus, New boundary conditions for the c=-2 ghost system, Phys. Rev. D77 (2008) 026003.


[2.] T. Creutzig, T. Quella and V. Schomerus, Branes in the GL(1|1) WZNW-Model, Nucl. Phys. B792 (2008) 257-283.


[3.] T. Creutzig, T. Quella and V. Schomerus, Boundary Spectra in Superspace Sigma-Models, JHEP 0810 (2008) 024.


[4.] T. Creutzig and V. Schomerus, Boundary Correlators in Supergroup WZNW Models, Nucl. Phys. B807 (2009) 471-494.


[5.] T. Creutzig, Geometry of branes on supergroups. Nucl. Phys. B812 (2009) 301-321.


[6.] T. Creutzig and P. B. Ronne, The GL(1|1)-symplectic fermion correspondence, Nucl. Phys. B815 (2009) 95-124.


[7.] T. Creutzig, P. B. Ronne and V. Schomerus, N=2 Superconformal Symmetry in Super Coset Models, Phys. Rev. D80 (2009) 066010.


[8.] T. Creutzig, C. Candu, V. Mitev and V. Schomerus, Cohomological Reduction of Sigma Models, JHEP 1005 (2010) 047.


[9.] T. Creutzig and Y. Hikida, Branes in the OSP(1|2) WZNW model, Nucl.Phys. B842 (2011).


[10.] T. Creutzig and P. B. Ronne, From world-sheet supersymmetry to super target spaces, JHEP 1011 (2010) 021.


[11.] T. Creutzig, J. Corn and L. Dolan, Yangian in the Twistor String, JHEP 1010 (2010) 076.


[12.] T. Creutzig, Yangian Superalgebras in Conformal Field Theory. Nucl. Phys. B849 (2011) 636-653.


[13.] T. Creutzig, Y. Hikida and P. B. Ronne, The FZZ duality with boundary, JHEP 1109 (2011) 004.


[14.] T. Creutzig, Y. Hikida and P. B. Ronne, Supergroup - extended super Liouville correspondence, JHEP 1106 (2011).


[15.] T. Creutzig, Y. Hikida and P. B. Ronne, Higher spin AdS_3 supergravity and its dual CFT, JHEP 1202 (2012) 109.


[16.] T. Creutzig, P. Gao and A. Linshaw, Fermionic Coset, Critical Level W^{(2)}_4-Algebra and Higher Spins, JHEP 1204 (2012) 031.


[17.] T. Creutzig and D. Ridout, Modular Data and Verlinde Formulae for Fractional Level WZW Models I, Nucl. Phys. B 865 (2012) 83.


[18.] T. Creutzig, Y. Hikida and P. B. Ronne, Three point functions in higher spin AdS_3 supergravity, JHEP 1301 (2013) 171.


[19.] T. Creutzig, Y. Hikida and P. B. Ronne, N=1 supersymmetric higher spin holography on AdS_3, JHEP 1302 (2013) 019.


[20.] T. Creutzig and D. Ridout, Relating the Archetypes of Logarithmic Conformal Field Theory, Nucl. Phys. B 872 (2013) 348.


[21.] T. Creutzig and D. Ridout, Modular Data and Verlinde Formulae for Fractional Level WZW Models II, Nucl. Phys. B 875 (2013) 423.


[22.] T. Creutzig, Y. Hikida and P. B. Ronne, Extended higher spin holography and Grassmannian models, JHEP 1311 (2013) 038.


[23.] H. Afshar, T. Creutzig, D. Grumiller, Y. Hikida and P. B. Ronne, Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry, JHEP 1406 (2014) 063.


[24.] T. Creutzig, Y. Hikida and P. B. Ronne, Higher spin AdS_3 holography with extended supersymmetry, JHEP 1410 (2014) 163.


[25.] T. Creutzig and Y. Hikida, Higgs phenomenon for higher spin fields on AdS_3, JHEP 1510 (2015) 164.


[26.] T. Creutzig, Y. Hikida and P. B. Ronne, Correspondences between WZNW models and CFTs with W-algebra symmetry, JHEP 1602 (2016) 048.


[27.] T. Creutzig, S. Kanade, T. Liu and D. Ridout, Cosets, characters and fusion for admissible-level osp(1 |2) minimal models, Nucl. Phys. B 938 (2019) 22.


[28.] T. Creutzig, Logarithmic W-algebras and Argyres-Douglas theories at higher rank, JHEP 1811 (2018) 188.


[29.] K. Costello, T. Creutzig and D. Gaiotto, Higgs and Coulomb branches from vertex operator algebras, JHEP 1903 (2019) 066.


[30.] T. Creutzig and Y. Hikida, Rectangular W-algebras, extended higher spin gravity and dual coset CFTs, JHEP 1902 (2019) 147.


[31.] T. Creutzig, T. Liu, D. Ridout and S. Wood, Unitary and non-unitary N=2 minimal models, JHEP 1906 (2019) 024.


[32.] T. Creutzig, Y. Hikida and T. Uetoko, Rectangular W-algebras of types so(M) and sp(2M) and dual coset CFTs, accepted in JHEP.

[33.] T.~Creutzig and Y.~Hikida, Rectangular W-(super)algebras and their representations, accepted in  Phys. Rev. D.


M A T H E M A T I C A L   P H Y S I C S



[1.] T. Creutzig, A. Klauer and N. R. Scheithauer, Natural constructions of some generalized Kac-Moody algebras as bosonic strings, Commun. Num. Theor. Phys. 1 (2007) 453-477.


[2.] T. Creutzig and D. Ridout, Logarithmic Conformal Field Theory: Beyond an Introduction, J. Phys. A 46 (2013), no. 49, 494006.


[3.] T. Creutzig, D. Ridout and S. Wood, Coset Constructions of Logarithmic (1,p)-Models, Lett. Math. Phys. 104, 5 (2014) 553-583.


[4.] T. Creutzig and G. Hohn, Mathieu Moonshine and the Geometry of K3 Surfaces, Commun. Num. Theor. Phys. 8, 2 (2014) 295-328.


[5.] A. Babichenko and T. Creutzig, Harmonic analysis and free field realization of the takiff supergroup of GL(1|1), SIGMA 11 (2015) 067.


[6.] V. Bouchard, T. Creutzig, D. E. Diaconescu, C. Doran, C. Quigley and A. Sheshmani, Vertical D4-D2-D0 bound states on K3 fibrations and modularity, Comm. Math. Phys. 350 (2017), no. 3, 1069-1121.


[7.] T. Arakawa, T. Creutzig, K. Kawasetsu and A. Linshaw, Orbifolds and Cosets of Minimal W-Algebras. Comm. Math. Phys. 355 (2017), no. 1, 339-372.


[8.] T. Creutzig and T. Gannon, Logarithmic conformal field theory, log-modular tensor categories and modular forms, J.Phys. A50 (2017) no.40, 404004.


[9.] T. Creutzig, J. F. R. Duncan and W. Riedler, Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory, J. Phys. A 51 (2018) no.3, 034001.


[10.] T. Creutzig, Y.-Z. Huang and J. Yang, Braided tensor categories of admissible modules for affine Lie algebras, Commun. Math. Phys. 362 (2018) no.3, 827.


[11.] J. Auger, T. Creutzig and D. Ridout, Modularity of logarithmic parafermion vertex algebras, Lett. Math. Phys. 108 (2018) no.12, 2543.


[12.] V. Bouchard, T. Creutzig and A. Joshi, Hecke Operators on Vector-Valued Modular Forms, SIGMA 15 (2019) 041.



S U B M I T T E D



[13.] J. Auger, T. Creutzig, S. Kanade and M. Rupert, Braided Tensor Categories related to B_p Vertex Algebras.


[14.] T. Creutzig, D. Gaiotto and A. R. Linshaw, S-duality for the large N=4 superconformal algebra.


[15.] T. Creutzig and D. Gaiotto, Vertex Algebras for S-duality.



M A T H E M A T I C S



[1.] C. Alfes and T. Creutzig, The Mock Modular Data of a Family of Superalgebras, Proc. Amer. Math. Soc. 142 (2014), 2265-2280.


[2.] T. Creutzig, P. Gao and A. Linshaw, A commutant realization of W^(2)_n at critical level, Int. Math. Res. Not. IMRN 2014, no. 3, 577-609.


[3.] T. Creutzig and A. Linshaw, A commutant realization of Odake's-algebra, Transform. Groups 18 (2013), no. 3, 615-637.


[4.] T. Creutzig and A. Linshaw, The super W_{1+\infty} algebra with integral central charge, Trans. Amer. Math. Soc. 367 (2015), no. 8, 5521-5551.


[5.] T. Creutzig, G. Hohn and T. Miezaki, The McKay-Thompson series of Mathieu Moonshine modulo two, The Ramanujan Journal 34, 3 (2014) 319-328.


[6.] T. Creutzig and A. Milas, False Theta Functions and the Verlinde formula, Advances in Mathematics 262 (2014) 520-545.


[7.] K. Bringmann, T. Creutzig and L. Rolen, Negative Index Jacobi Forms and Quantum Modular Forms, Research in the Mathematical Sciences (2014), 1:11.


[8.] T. Creutzig and A. Linshaw, Orbifolds of symplectic fermion algebras, Trans. Am. Math. Soc. 369, No. 1 (2017), 467-494.


[9.] T. Creutzig, A. Milas and S. Wood, On Regularised Quantum Dimensions of the Singlet Vertex Operator Algebra and False Theta Functions, Int. Math. Res. Not. IMRN 2017, no. 5, 1390-1432.


[10.] T. Creutzig and A. Milas, Higher rank partial and false theta functions and representation theory. Adv. Math. 314 (2017), 203-227.


[11.] T. Arakawa, T. Creutzig and A. Linshaw, Cosets of Bershadsky-Polyakov algebras and rational W-algebras of type A, Selecta Mathematica 23 (4), 2369-2395.


[12.] T. Creutzig, W-algebras for Argyres-Douglas theories, European Journal of Mathematics 3 (3), (2017), 659-690.


[13.] T. Creutzig, A. Milas and M. Rupert, Logarithmic Link Invariants of \overline{U}_q^H({sl}_2) and Asymptotic Dimensions of Singlet Vertex Algebras, Journal of Pure and Applied Algebra, 222, 10, (2018), 3224-3247.


[14.] T. Creutzig, S. Kanade, A. R. Linshaw and D. Ridout, Schur-Weyl Duality for Heisenberg Cosets, Transform. Groups 24 (2019), no. 2, 301--354.


[15.] T. Creutzig, J. Frohlich, S. Kanade, Representation theory of L_k(osp(1 | 2)) from vertex tensor categories and Jacobi forms, Proc. Am. Math. Soc. 146 (2018) no.11, 4571.


[16.] T. Creutzig and A. Linshaw, Cosets of affine vertex algebras inside larger structures, Journal of Algebra 517 (2019) 396-438.


[17.] T. Creutzig, S. Kanade and A. Linshaw, Simple current extensions beyond semi-simplicity, Accepted in Communications in Contemporary Mathematics.


[18.] T. Creutzig, A. Gainutdinov and I. Runkel, A quasi-Hopf algebra for the triplet vertex operator algebra, Accepeted in Communications in Contemporary Mathematics.


[19.] T. Creutzig, Fusion categories for affine vertex algebras at admissible levels, Sel. Math. New Ser. (2019) 25: 27.


[20.] T. Arakawa, T. Creutzig and A. Linshaw, W-algebras as coset vertex algebras, Invent. math. (2019) 218: 145.


S U B M I T T E D


[21.] W. Y. Chuang, T. Creutzig, D. E. Diaconescu and Y. Soibelman, Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and W-algebras.


[22.] T. Creutzig, S. Kanade and R. McRae, Gluing vertex algebras.


[23.] G. Borot, V. Bouchard, N. K. Chidambaram, T. Creutzig and D. Noshchenko, Higher Airy structures, W algebras and topological recursion.


[24.] T. Creutzig, S. Kanade and R. McRae, Tensor categories for vertex operator superalgebra extensions.

[25.] T. Creutzig, B. Feigin and A. R. Linshaw, N=4 superconformal algebras and diagonal cosets.

[26.] T. Creutzig, A. R. Linshaw and W. Riedler, Invariant subalgebras of the small N=4 superconformal algebra.


B O O K  E D I T E D


[1.] T. Creutzig and A. R. Linshaw, Vertex Algebras and Geometry, Contemporary Mathematics 711 (2018).



P R O C E E D I N G S

[1.] T. Creutzig, Quantum Dimensions in Logarithmic CFT, Oberwolfach report No. 16 (2015) 52--54, pdf

[2.] T. Creutzig, Y. Hikida and P. B. Ronne, Higher spin AdS3 holography and superstring theory,  pdf

[3.] T. Creutzig and D. Ridout, W-algebras extending affine gl(1|1), Springer Proc. Math. Stat. 36 (2013), pdf

[4.] T. Creutzig, Y. Hikida and P. B. Ronne, Higher Spin AdS_3 Supergravity and its CFT dual, Int. J. Mod. Phys. Conf. Ser. 21 (2013) 163-164, pdf

[5.] T. Creutzig and A. Linshaw, Cosets of the W^k(sl_4, f_{subreg})-algebra, Contemp. Math. 711 (2018), 105-117.


T H E S E S


T. Creutzig, Branes in supergroups, Doktorarbeit, pdf

T. Creutzig, Natural constructions of some generalized Kac-Moody algebras as bosonic strings, Diplomarbeit, pdf