4-manifolds and topological modular forms

Sergei Gukov; Du Pei; Pavel Putrov; Cumrun Vafa

doi:10.1007/JHEP05(2021)084

4-manifolds and topological modular forms

Sergei Gukov, Du Pei^*, Pavel Putrov, Cumrun Vafa

^*Corresponding author af dette arbejde

Institut for Matematik - Center for Kvantegeometri af Modulirum

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

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.

Originalsprog	Engelsk
Artikelnummer	84
Tidsskrift	Journal of High Energy Physics
Vol/bind	2021
Nummer	5
ISSN	1126-6708
DOI	https://doi.org/10.1007/JHEP05(2021)084
Status	Udgivet - maj 2021

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title = "4-manifolds and topological modular forms",

abstract = "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 {\textquoteright}t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.",

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author = "Sergei Gukov and Du Pei and Pavel Putrov and Cumrun Vafa",

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T1 - 4-manifolds and topological modular forms

AU - Gukov, Sergei

AU - Pei, Du

AU - Putrov, Pavel

AU - Vafa, Cumrun

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

KW - Anomalies in Field and String Theories

KW - Conformal Field Theory

KW - Differential and Algebraic Geometry

KW - Topological Field Theories

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U2 - 10.1007/JHEP05(2021)084

DO - 10.1007/JHEP05(2021)084

M3 - Journal article

AN - SCOPUS:85105708139

SN - 1126-6708

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 5

M1 - 84

ER -

4-manifolds and topological modular forms

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