Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants - INSPIRE

DataBETA

Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants

May 11, 2020

34 pages

Published in:

J.Geom.Phys. 168 (2021) 104311

Published: Oct, 2021

e-Print:

2005.05347 [hep-th]

DOI:

10.1016/j.geomphys.2021.104311 (publication)

View in:

ADS Abstract Service

reference search49 citations

Citations per year

Abstract: (Elsevier B.V.)

By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. This opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.

Note:

33 pages, 1 figure, 7 tables

Equivariant index formula
Verlinde formula
Rozansky-Witten theory
ADO invariants
space: noncompact
geometry: affine
Coulomb
Grassmann
knot theory
dimension: 3

References(90)

Figures(1)

[1]

Y. Akutsu
,
T. Deguchi
,
T. Ohtsuki

- J. Knot Theory Ramif. 1 (1992) 161

[2]

The Verlinde formula for Higgs bundles

Jørgen Ellegaard Andersen
(
- Aarhus U., Math. Sci.
)
,
Sergei Gukov
(
- Bonn, Max Planck Inst., Math. and
- Caltech
)
,
Du Pei
(
- Aarhus U., Math. Sci. and
- Caltech
)

e-Print:
- 1608.01761

[3]

S. Arkhipov
,
R. Bezrukavnikov
,
V. Ginzburg

- J.Am.Math.Soc. 17 (2004) 595

[4]

Lezioni Lincee [Lincei Lectures]

M. Atiyah

•
DOI:
- 10.1017/CBO9780511623868

[5]

A topologically twisted index for three-dimensional supersymmetric theories

Francesco Benini
(
- Amsterdam U. and
- Imperial Coll., London
)
,
Alberto Zaffaroni
(
- INFN, Milan Bicocca and
- Milan Bicocca U.
)

- JHEP 07 (2015) 127
•
e-Print:
- 1504.03698
•
DOI:
- 10.1007/JHEP07(2015)127

[6]

Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

Sergio Benvenuti
(
- MIT, LNS and
- Princeton U.
)
,
Bo Feng
(
- Imperial Coll., London and
- Zhejiang U.
)
,
Amihay Hanany
(
- MIT, LNS
)
,
Yang-Hui He
(
- Oxford U. and
- Oxford U., Inst. Math.
)

- JHEP 11 (2007) 050
•
e-Print:
- hep-th/0608050
•
DOI:
- 10.1088/1126-6708/2007/11/050

[7]

R. Bezrukavnikov
,
A. Lachowska

- Contemp.Math. vol. 433 (2007) 89-101
•
DOI:
- 10.1090/conm/433/08322

[8]

R. Bezrukavnikov
,
M. Finkelberg
,
I. Mirković

- Compos.Math. 141 (2005) 746

[9]

Aspects of N(T) >= two topological gauge theories and D-branes

- Nucl.Phys.B 492 (1997) 545-590
•
e-Print:
- hep-th/9612143
•
DOI:
- 10.1016/S0550-3213(97)00161-2

[10]

On the relationship between the Rozansky-Witten and the three-dimensional Seiberg-Witten invariants

Matthias Blau
(
- ICTP, Trieste
)
,
George Thompson
(
- ICTP, Trieste
)

- Adv.Theor.Math.Phys. 5 (2002) 483-498
•
e-Print:
- hep-th/0006244
•
DOI:
- 10.4310/ATMP.2001.v5.n3.a3

[11]

Pursuing the Double Affine Grassmannian I: Transversal Slices via Instantons on $A_k$ -Singularities

- Duke Math.J. 152 (2010) 175-206
•
e-Print:
- 0711.2083
•
DOI:
- 10.1215/00127094-2010-011

[12]

A. Braverman
,
M. Finkelberg
,
D. Gaitsgory

- Progr.Math. vol. 244 (2006) 17-135
•
DOI:
- 10.1007/0-8176-4467-9_2

[13]

Towards a mathematical definition of Coulomb branches of $3$ -dimensional $\mathcal{N} = 4$ gauge theories, II

- Adv.Theor.Math.Phys. 22 (2018) 1071-1147
•
e-Print:
- 1601.03586
•
DOI:
- 10.4310/ATMP.2018.v22.n5.a1

[14]

Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian

- Adv.Theor.Math.Phys. 23 (2019) 75-166
•
e-Print:
- 1604.03625
•
DOI:
- 10.4310/ATMP.2019.v23.n1.a3

[15]

Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)

Alexander Braverman
(
- Toronto U., Math. Dept. and
- Perimeter Inst. Theor. Phys.
)
,
Michael Finkelberg
(
- Skoltech and
- Higher Sch. of Economics, Moscow
)
,
Hiraku Nakajima
(
- Kyoto U., RIMS
)

- Physics 23 (2019) 253-344
•
e-Print:
- 1706.02112

[16]

The ADO Invariants are a q-Holonomic Family

Jennifer Brown
(
- UC, Davis, Dept. Math. and
- UC, Davis, QMAP
)
,
Tudor Dimofte
(
- UC, Davis, Dept. Math. and
- UC, Davis, QMAP
)
,
Stavros Garoufalidis
(
- Bonn, Max Planck Inst., Math. and
- SUSTech, Shenzhen
)
,
Nathan Geer
(
- Utah State U.
)

e-Print:
- 2005.08176

[17]

The Coulomb Branch of 3d ${\mathcal{N}= 4}$ Theories

- Commun.Math.Phys. 354 (2017) 2, 671-751
•
e-Print:
- 1503.04817
•
DOI:
- 10.1007/s00220-017-2903-0

[18]

Twisted indices of 3d $\mathcal{N}$ = 4 gauge theories and enumerative geometry of quasi-maps

- JHEP 07 (2019) 014
•
e-Print:
- 1812.05567
•
DOI:
- 10.1007/JHEP07(2019)014

[19]

E. Calabi

- Ann. Sci. Éc. Norm. Supér. (4) 12 (1979) 269

[20]

Paper No. 134, 16

J. Chae

- SIGMA 16 (2020)

[21]

J. Cheeger

- Ann. Math. (2) 109 (1979) 259

[22]

3d Modularity

Miranda C.N. Cheng
(
- Amsterdam U.
)
,
Sungbong Chun
(
- Caltech
)
,
Francesca Ferrari
(
- Amsterdam U.
)
,
Sergei Gukov
(
- Caltech
)
,
Sarah M. Harrison
(
- Hefei, CUST and
- McGill U.
)

- JHEP 10 (2019) 010
•
e-Print:
- 1809.10148
•
DOI:
- 10.1007/JHEP10(2019)010

[23]

J. Cho
,
J. Murakami

- J. Knot Theory Ramif. 18 (2009) 1271

[24]

3d-3d correspondence for mapping tori

Sungbong Chun
(
- Rutgers U., Piscataway
)
,
Sergei Gukov
(
- Caltech and
- Bonn, Max Planck Inst., Math.
)
,
Sunghyuk Park
(
- Caltech
)
,
Nikita Sopenko
(
- Caltech
)

- JHEP 09 (2020) 152
•
e-Print:
- 1911.08456
•
DOI:
- 10.1007/JHEP09(2020)152

[25]

BPS Invariants for Seifert Manifolds

Hee-Joong Chung
(
- Tsinghua U., Beijing
)

- JHEP 03 (2020) 113
•
e-Print:
- 1811.08863
•
DOI:
- 10.1007/JHEP03(2020)113

1-25 of 90
1
2
3
4
25 / page