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2018

Landau-Ginzburg models for certain fiber products with curves

Chen, Zhuo, Pantev, Tony, Sharpe, Eric

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In this paper we describe a physical realization of a family of non-compact Kahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburg models, motivated by some recent non-Kahler solutions of Strominger systems, and utilizing some recent ideas from GLSMs.

We consider threefolds given as fiber products of compact genus g Riemann surfaces and noncompact threefolds.
Each genus g Riemann surface is constructed using recent GLSM tricks, as a double cover of P^1 branched over a degree 2g + 2 locus, realized via nonperturbative effects rather than as the critical locus of a superpotential.
We focus in particular on special cases corresponding to a set of Kahler twistor spaces of certain hyperKahler four-manifolds, specifically the twistor spaces of R^4, C^2/Z_k, and S^1 x R^3.

Landau-Ginzburg models for certain fiber products with curves · Around

Built on

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N. Hitchin, “Twistor construction of Einstein metrics,” in Global Riemannian geometry (Durham, 1983)
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Similar

A. Strominger, “Superstrings with Torsion,” Nucl. Phys. B 274
1986
Cited alongside, same era.
G. Farkas, “Gaussian maps, Gieseker-Petri loci and large theta-characteristics,” J. Reine Angew. Math. 581
2005
Cited alongside, same era.
T. Pantev and E. Sharpe, “GLSM’s for Gerbes (and other toric stacks),” Adv. Theor. Math. Phys. 10
2006
Cited alongside, same era.
T. Fei, Z. Huang and S. Picard, “A Construction of Infinitely Many Solutions to the Strominger System,” [arXiv:1703.10067 [math.DG]]
Original
Cited in the paper.
P. Gao, S.-T. Yau, W. Zhou, “Nonexistence for complete Kähler Einstein metrics on some noncompact manifolds,” arXiv: 1603.09135
Cited in the paper.

Then

S. Hellerman, A. Henriques, T. Pantev, E. Sharpe and M. Ando, “Cluster decomposition, T-duality, and gerby CFT’s,” Adv. Theor. Math. Phys. 11
2007
Later among the works it cites.
A. Caldararu, J. Distler, S. Hellerman, T. Pantev and E. Sharpe, “Non-birational twisted derived equivalences in abelian GLSMs,” Commun. Math. Phys. 294
Original
2010
Later among the works it cites.
L. B. Anderson, B. Jia, R. Manion, B. Ovrut and E. Sharpe, “General aspects of heterotic string compactifications on stacks and gerbes,” Adv. Theor. Math. Phys. 19
Original
2015
Later among the works it cites.

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