Equivariant K3 invariants

Cheng, Miranda C.  N.; Duncan, John F.  R.; Harrison, Sarah M.; Kachru, Shamit

doi:10.4310/CNTP.2017.v11.n1.a2

Title: Equivariant K3 invariants

Abstract

In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau–Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz–Klemm–Vafa (KKV), and Katz–Klemm–Pandharipande (KKP). We show that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been observed to give rise to mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway’s group. We also study equivariant versions of these invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel–Hohenegger–Volpato, and one may consider corresponding equivariant refined K3 Gopakumar–Vafa invariants. The same symmetries naturally arise in the auxiliary CFT state space, affording a suggestive alternative view of the same computation. We comment on a lift of this story to the generating function of ellipticmore »« less

Authors:

Cheng, Miranda C. N. ^[1]; Duncan, John F. R. ^[2]; Harrison, Sarah M. ^[3]; Kachru, Shamit ^[4]

Univ. of Amsterdam (Netherlands); Centre National de la Recherche Scientifique (CNRS), Paris (France)
Emory Univ., Atlanta, GA (United States)
Harvard Univ., Cambridge, MA (United States)
Stanford Univ., CA (United States)

Publication Date:: Sun Jan 01 00:00:00 EST 2017

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1378561

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Communications in Number Theory and Physics

Additional Journal Information:: Journal Volume: 11; Journal Issue: 1; Journal ID: ISSN 1931-4523

Publisher:: International Press

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Cheng, Miranda C.  N., Duncan, John F.  R., Harrison, Sarah M., and Kachru, Shamit. Equivariant K3 invariants.  United States: N. p., 2017. 
Web.  doi:10.4310/CNTP.2017.v11.n1.a2.

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                    Cheng, Miranda C.  N., Duncan, John F.  R., Harrison, Sarah M., & Kachru, Shamit. Equivariant K3 invariants.  United States.  https://doi.org/10.4310/CNTP.2017.v11.n1.a2

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                    Cheng, Miranda C.  N., Duncan, John F.  R., Harrison, Sarah M., and Kachru, Shamit. Sun .  
"Equivariant K3 invariants".  United States.  https://doi.org/10.4310/CNTP.2017.v11.n1.a2.  https://www.osti.gov/servlets/purl/1378561.

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@article{osti_1378561,

  title        = {Equivariant K3 invariants},

  author       = {Cheng, Miranda C.  N. and Duncan, John F.  R. and Harrison, Sarah M. and Kachru, Shamit},

  abstractNote = {In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformal field theory. We consider the invariants calculated by Yau–Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz–Klemm–Vafa (KKV), and Katz–Klemm–Pandharipande (KKP). We show that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been observed to give rise to mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway’s group. We also study equivariant versions of these invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel–Hohenegger–Volpato, and one may consider corresponding equivariant refined K3 Gopakumar–Vafa invariants. The same symmetries naturally arise in the auxiliary CFT state space, affording a suggestive alternative view of the same computation. We comment on a lift of this story to the generating function of elliptic genera of symmetric products of K3 surfaces.},

  doi          = {10.4310/CNTP.2017.v11.n1.a2},

  journal      = {Communications in Number Theory and Physics},

  number       = 1,

  volume       = 11,

  place        = {United States},

  year         = {Sun Jan 01 00:00:00 EST 2017},

  month        = {Sun Jan 01 00:00:00 EST 2017}

}

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Works referencing / citing this record:

Gravitational couplings in N = 2 $$ \mathcal{N}=2 $$ string compactifications and Mathieu Moonshine
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A Borcherds–Kac–Moody Superalgebra with Conway Symmetry
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Harrison, Sarah M.; Paquette, Natalie M.; Volpato, Roberto
Communications in Mathematical Physics, Vol. 370, Issue 2
DOI: 10.1007/s00220-019-03518-0

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Citation Formats

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