Analogues of Mathai-Quillen forms in sheaf cohomology and applications to topological field theory. (English) Zbl 1316.81082
Summary: We construct sheaf-cohomological analogues of Mathai-Quillen forms, that is, holomorphic bundle-valued differential forms whose cohomology classes are independent of certain deformations, and which are believed to possess Thom-like properties. Ordinary Mathai-Quillen forms are special cases of these constructions, as we discuss. These sheaf-theoretic variations arise physically in A/2 and B/2 model pseudo-topological field theories, and we comment on their origin and role.
MSC:
| 81T45 | Topological field theories in quantum mechanics |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 53C65 | Integral geometry |
| 14F10 | Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials |
| 18F20 | Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) |
References:
| [1] | Mathai, V.; Quillen, D., Superconnections, Thom classes, and equivariant differential forms, Topology, 25, 85-110 (1986) · Zbl 0592.55015 |
| [2] | Kalkman, J., BRST model for equivariant cohomology and representatives for the equivariant Thom class, Comm. Math. Phys., 153, 447-463 (1993) · Zbl 0776.55003 |
| [3] | Blau, M., The Mathai-Quillen formalism and topological field theory, J. Geom. Phys., 11, 95-127 (1993) · Zbl 0780.57024 |
| [4] | Wu, S., On the Mathai-Quillen formalism of topological sigma models, J. Geom. Phys., 17, 299-309 (1995) · Zbl 0838.58006 |
| [5] | Cordes, S.; Moore, G.; Ramgoolam, S., Lectures on 2D Yang-Mills theory, equivariant cohomology and topological field theories, Nucl. Phys. Proc. Suppl., 41, 184-244 (1995) · Zbl 0991.81585 |
| [6] | Wu, S., Mathai-Quillen formalism · Zbl 0838.58006 |
| [7] | Katz, S.; Sharpe, E., Notes on certain \((0, 2)\) correlation functions, Comm. Math. Phys., 262, 611-644 (2006) · Zbl 1109.81066 |
| [8] | Adams, A.; Distler, J.; Ernebjerg, M., Topological heterotic rings, Adv. Theor. Math. Phys., 10, 657-682 (2006) · Zbl 1116.81049 |
| [9] | Sharpe, E., Notes on certain other \((0, 2)\) correlation functions, Adv. Theor. Math. Phys., 13, 33-70 (2009) · Zbl 1171.81420 |
| [10] | McOrist, J.; Melnikov, I. V., Summing the instantons in half-twisted linear sigma models, J. High Energy Phys., 02, 026 (2009) · Zbl 1245.81249 |
| [11] | Donagi, R.; Guffin, J.; Katz, S.; Sharpe, E., A mathematical theory of quantum sheaf cohomology · Zbl 1300.32022 |
| [12] | Donagi, R.; Guffin, J.; Katz, S.; Sharpe, E., Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties · Zbl 1306.81217 |
| [13] | Melnikov, I.; Sethi, S.; Sharpe, E., Recent developments in \((0, 2)\) mirror symmetry, SIGMA, 8, 068 (2012) · Zbl 1271.32020 |
| [14] | Guffin, J.; Sharpe, E., A-twisted Landau-Ginzburg models, J. Geom. Phys., 59, 1547-1580 (2009) · Zbl 1187.81188 |
| [15] | Guffin, J.; Sharpe, E., A-twisted heterotic Landau-Ginzburg models, J. Geom. Phys., 59, 1581-1596 (2009) · Zbl 1187.81189 |
| [16] | Ando, M.; Sharpe, E., Elliptic genera of Landau-Ginzburg models over nontrivial spaces, Adv. Theor. Math. Phys., 16, 1087-1144 (2012) · Zbl 1283.35132 |
| [17] | Clarke, P., Duality for toric Landau-Ginzburg models · Zbl 1386.81130 |
| [18] | Bertolini, M.; Melnikov, I.; Plesser, R., Hybrid conformal field theories · Zbl 1333.81312 |
| [19] | Berline, N.; Getzler, E.; Vergne, M., (Heat Kernels and Dirac Operators. Heat Kernels and Dirac Operators, Grund. der Math. Wiss., vol. 298 (1992), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York) · Zbl 0744.58001 |
| [22] | Distler, J.; Greene, B.; Morrison, D., Resolving singularities in \((0, 2)\) models, Nuclear Phys. B, 481, 289-312 (1996) · Zbl 1049.81585 |
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