Eric Sharpe in nLab

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Eric Sharpe works on theoretical physics related to string theory with an emphasis on structural aspects and mathematical formalization. He got his Phd under Edward Witten.

Sharpe has early on realized the role of higher differential geometry in the form of stacks and gerbes in string theory. He identified string theorists’s “discrete torsion” with the equivariant cohomology of bundle gerbes on orbifolds (Sharpe 99, Sharpe 01) and he was the first to consider the possibility that target spaces for string sigma-models may themselves be stacks/gerbes (Pantev-Sharpe 05a, Pantev-Sharpe 05b, Hellerman-Sharpe 10).

More recently he has been investigating quantum sheaf cohomology.

In (Sharpe 15) he lays out a general perspective of the role of 2-group and generally n-group (infinity-group) global higher gauge symmetry in quantum field theory and string theory.

Selected writings

On discrete torsion:

• Eric Sharpe, Discrete torsion, Phys.Rev. D68 (2003) 126003 (arXiv:hep-th/0008154)

• Eric Sharpe, Discrete Torsion and Gerbes I (arXiv:hep-th/9909108)

  Discrete Torsion and Gerbes II (arXiv:hep-th/9909120)

On stacks as target spaces for sigma-models:

• Eric Sharpe, Discrete Torsion, Quotient Stacks, and String Orbifolds (arXiv:math/0110156)

• Tony Pantev, Eric Sharpe, String compactifications on Calabi-Yau stacks, Nucl.Phys. B733 (2006) 233-296, (arXiv:hep-th/0502044)

• Tony Pantev, Eric Sharpe, Gauged linear sigma-models for gerbes (and other toric stacks), (arXiv:hep-th/0502053)

• S. Hellerman, Eric Sharpe, Sums over topological sectors and quantization of Fayet-Iliopoulos parameters, (arXiv:1012.5999)

• Eric Sharpe, Notes on generalized global symmetries in QFT (arXiv:1508.04770)

On heterotic string vacua:

• Eric Sharpe, Recent developments in heterotic compactifications, AMS/IP Stud. Adv. Math. 44 (2008) 209-230 (arXiv:0801.4080)

On elliptic genera of Landau-Ginzburg models:

• Matthew Ando, Eric Sharpe, Elliptic genera of Landau-Ginzburg models over nontrivial spaces, Adv. Theor. Math. Phys. 16 (2012) 1087-1144 (arXiv:0905.1285)

On quantum sheaf cohomology:

• Ron Donagi, Josh Guffin, Sheldon Katz, Eric Sharpe, A Mathematical Theory of Quantum Sheaf Cohomology, Asian J. Math. 18 (2014) 387-418 [arXiv:1110.3751, doi:10.4310/AJM.2014.v18.n3.a1]

On duality in string theory in view of category theory and higher geometry:

• Eric Sharpe, Categorical Equivalence and the Renormalization Group, Proceedings of LMS/EPSRC Symposium Higher Structures in M-Theory, Fortschritte der Physik 2019 (arXiv:1903.02880)

Discussion of the Hilbert schemes of points of ADE-singularities:

• Ron Donagi, Sheldon Katz, Eric Sharpe, Spectra of D-branes with Higgs vevs, Adv.Theor.Math.Phys. 8 (2005) 813-859 (arXiv:hep-th/0309270)

On orbifolds by 2-groups in view of sigma-models inspired from string theory:

• Alonso Perez-Lona, Eric Sharpe, Three-dimensional orbifolds by 2-groups [arXiv:2303.16220]

On quantum K-theory rings:

• W. Gu, Leonardo C. Mihalcea, Eric Sharpe, H. Zou, Quantum K theory of symplectic Grassmannians [arXiv:2008.04909

On gauged linear sigma-models:

• Eric Sharpe, A survey of recent developments in GLSMs [arxiv:2401.11637]

Selected talks

• Eric Sharpe, Sigma models on gerbes, talk at Higher Structures in M-Theory, Durham, August 2018 (pdf slides, video recording)