4-manifolds and topological modular forms - INSPIRE

4-manifolds and topological modular forms

Sergei Gukov
(
- Caltech and
- Bonn, Max Planck Inst., Math.
)
,
Du Pei
(
- Caltech and
- Aarhus U., Math. Sci.
)
,
Pavel Putrov
(
- ICTP, Trieste and
- Princeton, Inst. Advanced Study
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept.
)

Nov 19, 2018

76 pages

Published in:

JHEP 05 (2021) 084

Published: May 11, 2021

e-Print:

1811.07884 [hep-th]

DOI:

10.1007/JHEP05(2021)084

Report number:

CALT-TH-2018-034

View in:

reference search44 citations

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Abstract: (Springer)

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on ’t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.

Note:

74 pages

Conformal Field Theory
Anomalies in Field and String Theories
Differential and Algebraic Geometry
Topological Field Theories
twist: topological
modular
compactification
dimension: 6
symmetry: flavor
differential forms

References(82)

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)
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