nLab Adrian Norbert Schellekens

• webpage

• articles on arXiv

Bert Schellekens has been working on 2d CFT and specifically SCFT in relation to model building in string phenomenology. In particular he studied RCFT-Gepner model-orbifold-compactifications of the heterotic string and of intersecting D-brane models (via boundary states) in the type II superstring.

Recognizing the abundance of semi-realistic models (Lerche-Lüst-Schellekens 86, Lerche-Lüst-Schellekens 87), Schellekens was maybe the first to recognize and definitely the first to make explicit the existence and relevance of the landscape of string theory vacua and to coin that term in the first place (Schellekens 98, see Schellekens 06, Schellekens 08, Schellekens 16) long before this became more widely appreciated.

Schellekens’ scans of the “landscape” of vertex-algebraically well-defined Gepner model KK-compactification (in the sense of Spectral Standard Models and String Compactifications) of the heterotic string and of intersecting D-brane models (via boundary states) of the type II superstring (Dijkstra-Huiszoon-Schellekens 04a, Dijkstra-Huiszoon-Schellekens 04b) showed that solid and substantial investigation into the landscape of string theory vacua is possible, worthwhile and probably necessary.

As an example, from Dijkstra-Huiszoon-Schellekens 04b, the following is a plot of standard model-like coupling constants in a computer scan of Gepner model-KK-compactification of intersecting D-brane models. The blue dot indicates the couplings in $SU(5)$-GUT theory. The faint lines are NOT drawn by hand, but reflect increased density of Gepner models as seen by the computer scan.

Selected writings

On heterotic string theory:

• Wolfgang Lerche, Dieter Lüst, Adrian Norbert Schellekens, Ten-dimensional heterotic strings from Niemeier lattices, Physics Letters B 181 1–2 (1986) 71-75 [doi:10.1016/0370-2693(86)91257-8, inspire:233203]

  (relation to Niemeier lattices)

• Wolfgang Lerche, Dieter Lüst, Bert Schellekens, Chiral Four-dimensional Heterotic Strings from Self-dual Lattices Nucl. Phys. B 287, 477, 1987 (pdf)

• Bert Schellekens, Classification of Ten-Dimensional Heterotic Strings, Phys.Lett. B277 (1992) 277-284 (arXiv:hep-th/9112006)

On the partition function of the superstring (heterotic string and type II string) as a modular form with values in the Chern character of the background field strengths (“character-valued partition function”, a little later called the elliptic genus/Witten genus) and relation to Green-Schwarz anomaly cancellation:

• A. N. Schellekens, Nicholas P. Warner, Anomalies, characters and strings, Nuclear Physics B Volume 287, 1987, Pages 317-361 (doi:10.1016/0550-3213(87)90108-8)

• A. N. Schellekens, Nicholas P. Warner, Anomalies and modular invariance in string theory, Physics Letters B 177 (3-4), 317-323, 1986 (doi:10.1016/0370-2693(86)90760-4)

• Wolfgang Lerche, Bengt Nilsson, A. N. Schellekens, Heterotic string-loop calculation of the anomaly cancelling term, Nuclear Physics B Volume 289, 1987, Pages 609-627 (doi:10.1016/0550-3213(87)90397-X)

• Wolfgang Lerche, Bengt Nilsson, A. N. Schellekens, Nicholas P. Warner, Anomaly cancelling terms from the elliptic genus, Nuclear Physics B Volume 299, Issue 1, 28 March 1988, Pages 91-116 (doi:10.1016/0550-3213(88)90468-3)

On classification of strongly rational holomorphic vertex operator algebras of central charge $\leq 24$ (of relevance in heterotic string theory and monstrous moonshine):

• Adrian Norbert Schellekens, Meromorphic $c = 24$ Conformal Field Theories, Commun. Math. Phys. 153 (1993) 159-186 [doi:10.1007/BF02099044]

On orientifold Gepner model string phenomenology:

• T.P.T. Dijkstra, L. R. Huiszoon, Bert Schellekens, Chiral Supersymmetric Standard Model Spectra from Orientifolds of Gepner Models, Phys.Lett. B609 (2005) 408-417 (arXiv:hep-th/0403196)

• T.P.T. Dijkstra, L. R. Huiszoon, Bert Schellekens, Supersymmetric Standard Model Spectra from RCFT orientifolds, Nucl.Phys.B710:3-57,2005 (arXiv:hep-th/0411129)

On the landscape of string theory vacua:

• Bert Schellekens, Naar een waardig slot, inauguration speech ar University of Nijmegen, September 1998, ISBN 90-9012073-4 (ubn:2066/18631)

• Bert Schellekens, The Landscape “avant la lettre” (arXiv:physics/0604134)

• Bert Schellekens, The Emperor’s Last Clothes?, Rept. Prog. Phys.71:072201, 2008 (arXiv:0807.3249)

• Bert Schellekens, Big Numbers in String Theory (arXiv:1601.02462)

On string phenomenology with orbifold/orientifold intersecting D-brane models and Gepner models:

• Fernando Marchesano, Bert Schellekens, Timo Weigand, D-brane and F-theory Model Building, in: Handbook of Quantum Gravity, Springer (2023) [arXiv:2212.07443]

related $n$Lab entries

• Gepner model

• intersecting D-brane model

• string phenomenology, GUT

• landscape of string theory vacua

• discrete torsion

category: people