Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective - INSPIRE

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Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

Dec 26, 2018

119 pages

Published in:

SciPost Phys. 6 (2019) 5, 052

Published: May 1, 2019

e-Print:

1812.10451 [hep-th]

DOI:

10.21468/SciPostPhys.6.5.052 (publication)

Report number:

YITP-SB-18-41

View in:

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Abstract: (arXiv)

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities

\mathbf{X}

and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to

\mathbf{X}

. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type

A_{M-1}

fibered over a real line, and the map between the K\"ahler parameters of

\mathbf{X}

and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA "reductions" give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity

\mathbf{X}

. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d

\mathcal{N}=1

gauge theories.

Note:

89 pages plus appendix, many figures; v2: corrected typos and added references; added comment in sec.4.3, SciPost version

Superconformal theories in higher dimensions
geometric engineering
dimension: 5
field theory: conformal
energy: low
singularity
M-theory
prepotential
D-brane: 6
supersymmetry: 1

References(99)

Figures(130)

[1]

Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics

Nathan Seiberg
(
- Rutgers U., Piscataway
)

- Phys.Lett.B 388 (1996) 753-760
•
e-Print:
- hep-th/9608111
•
DOI:
- 10.1016/S0370-2693(96)01215-4

[2]

Extremal transitions and five-dimensional supersymmetric field theories

David R. Morrison
(
- Duke U.
)
,
Nathan Seiberg
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 483 (1997) 229-247
•
e-Print:
- hep-th/9609070
•
DOI:
- 10.1016/S0550-3213(96)00592-5

[3]

Small instantons, Del Pezzo surfaces and type I-prime theory

Michael R. Douglas
(
- Rutgers U., Piscataway
)
,
Sheldon H. Katz
(
- Oklahoma State U.
)
,
Cumrun Vafa
(
- Rutgers U., Piscataway and
- Harvard U.
)

- Nucl.Phys.B 497 (1997) 155-172
•
e-Print:
- hep-th/9609071
•
DOI:
- 10.1016/S0550-3213(97)00281-2

[4]

Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces

- Nucl.Phys.B 497 (1997) 56-100
•
e-Print:
- hep-th/9702198
•
DOI:
- 10.1016/S0550-3213(97)00279-4

[5]

Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams

- JHEP 01 (1998) 002
•
e-Print:
- hep-th/9710116
•
DOI:
- 10.1088/1126-6708/1998/01/002

[6]

String theory dynamics in various dimensions

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- ,
- Nucl.Phys.B 443 (1995) 85-126,
•
e-Print:
- hep-th/9503124
•
DOI:
- 10.1201/9781482268737-32

[7]

Open p-branes

- ,
- Phys.Lett.B 383 (1996) 44-47,
•
e-Print:
- hep-th/9512059
•
DOI:
- 10.1201/9781482268737-13

[8]

M5-Branes, Toric Diagrams and Gauge Theory Duality

Ling Bao
(
- Chalmers U. Tech.
)
,
Elli Pomoni
(
- Humboldt U., Berlin, Inst. Math. and
- Humboldt U., Berlin
)
,
Masato Taki
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Futoshi Yagi
(
- SISSA, Trieste
)

- JHEP 04 (2012) 105
•
e-Print:
- 1112.5228
•
DOI:
- 10.1007/JHEP04(2012)105

[9]

5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory

- JHEP 03 (2014) 112
•
e-Print:
- 1311.4199
•
DOI:
- 10.1007/JHEP03(2014)112

[10]

Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions

Masato Taki
(
- Nishina Ctr., RIKEN
)

e-Print:
- 1401.7200

[11]

Lifting 4d dualities to 5d

Oren Bergman
(
- Technion
)
,
Gabi Zafrir
(
- Technion
)

- JHEP 04 (2015) 141
•
e-Print:
- 1410.2806
•
DOI:
- 10.1007/JHEP04(2015)141

[12]

Duality and enhancement of symmetry in 5d gauge theories

Gabi Zafrir
(
- Technion
)

- JHEP 12 (2014) 116
•
e-Print:
- 1408.4040
•
DOI:
- 10.1007/JHEP12(2014)116

[13]

Fiber-Base Duality and Global Symmetry Enhancement

Vladimir Mitev
(
- Humboldt U., Berlin, Inst. Math. and
- Humboldt U., Berlin
)
,
Elli Pomoni
(
- DESY and
- Natl. Tech. U., Athens
)
,
Masato Taki
(
- Nishina Ctr., RIKEN
)
,
Futoshi Yagi
(
- Korea Inst. Advanced Study, Seoul
)

- JHEP 04 (2015) 052
•
e-Print:
- 1411.2450
•
DOI:
- 10.1007/JHEP04(2015)052

[14]

5d and 6d SCFTs Have No Weak Coupling Limit

Chi-Ming Chang
(
- UC, Davis, QMAP
)

- JHEP 09 (2019) 016
•
e-Print:
- 1810.04169
•
DOI:
- 10.1007/JHEP09(2019)016

[15]

Geometric engineering of quantum field theories

Sheldon H. Katz
(
- Oklahoma State U.
)
,
Albrecht Klemm
(
- Chicago U., EFI
)
,
Cumrun Vafa
(
- Harvard U.
)

- Nucl.Phys.B 497 (1997) 173-195
•
e-Print:
- hep-th/9609239
•
DOI:
- 10.1016/S0550-3213(97)00282-4

[16]

Mirror symmetry and exact solution of 4-D N=2 gauge theories: 1.

S. Katz
(
- Oklahoma State U. and
- Mittag-Leffler Inst.
)
,
P. Mayr
(
- Princeton, Inst. Advanced Study
)
,
C. Vafa
(
- Harvard U.
)

- Adv.Theor.Math.Phys. 1 (1998) 53-114
•
e-Print:
- hep-th/9706110
•
DOI:
- 10.4310/ATMP.1997.v1.n1.a2

[17]

Matrix models, geometric engineering and elliptic genera

Timothy J. Hollowood
(
- Swansea U.
)
,
Amer Iqbal
(
- Harvard U., Phys. Dept.
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept.
)

- JHEP 03 (2008) 069
•
e-Print:
- hep-th/0310272
•
DOI:
- 10.1088/1126-6708/2008/03/069

[18]

Phases of Five-dimensional Theories, Monopole Walls, and Melting Crystals

Sergey A. Cherkis
(
- Arizona U.
)

- JHEP 06 (2014) 027
•
e-Print:
- 1402.7117
•
DOI:
- 10.1007/JHEP06(2014)027

[19]

6D SCFTs and Phases of 5D Theories

- JHEP 09 (2017) 147
•
e-Print:
- 1703.02981
•
DOI:
- 10.1007/JHEP09(2017)147

[20]

Three dimensional canonical singularity and five dimensional $\mathcal{N}$ = 1 SCFT

Dan Xie
(
- Harvard U., Dept. Math. and
- Harvard U., Phys. Dept.
)
,
Shing-Tung Yau
(
- Harvard U., Dept. Math. and
- Harvard U., Phys. Dept.
)

- JHEP 06 (2017) 134
•
e-Print:
- 1704.00799
•
DOI:
- 10.1007/JHEP06(2017)134

[21]

Rigid limit for hypermultiplets and five-dimensional gauge theories

Sergei Alexandrov
(
- U. Montpellier, L2C and
- CERN
)
,
Sibasish Banerjee
(
- IPhT, Saclay and
- Bonn, Max Planck Inst., Math.
)
,
Pietro Longhi
(
- Uppsala U.
)

- JHEP 01 (2018) 156
•
e-Print:
- 1710.10665
•
DOI:
- 10.1007/JHEP01(2018)156

[22]

Towards classification of 5d SCFTs: Single gauge node

- SciPost Phys. 14 (2023) 5, 122,
- SciPost Phys. 14 (2023) 122
•
e-Print:
- 1705.05836
•
DOI:
- 10.21468/SciPostPhys.14.5.122

[23]

On Geometric Classification of 5d SCFTs

Patrick Jefferson
(
- Harvard U., Phys. Dept.
)
,
Sheldon Katz
(
- Illinois U., Urbana, Math. Dept.
)
,
Hee-Cheol Kim
(
- Harvard U., Phys. Dept. and
- POSTECH, Pohang
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept.
)

- JHEP 04 (2018) 103
•
e-Print:
- 1801.04036
•
DOI:
- 10.1007/JHEP04(2018)103

[24]

Classifying $5d$ SCFTs via $6d$ SCFTs: Rank one

- JHEP 07 (2019) 178,
- JHEP 01 (2020) 153 (addendum)
•
e-Print:
- 1809.01650
•
DOI:
- 10.1007/JHEP07(2019)178

[25]

Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank

Lakshya Bhardwaj
(
- Harvard U.
)
,
Patrick Jefferson
(
- Harvard U.
)

- JHEP 10 (2019) 282
•
e-Print:
- 1811.10616
•
DOI:
- 10.1007/JHEP10(2019)282

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