Higher Symmetry and Gapped Phases of Gauge Theories - INSPIRE

DataBETA

Higher Symmetry and Gapped Phases of Gauge Theories

Anton Kapustin
(
- Caltech
)
,
Ryan Thorngren
(
- UC, Berkeley, Math. Dept.
)

Sep 18, 2013

25 pages

Published in:

Prog.Math. 324 (2017) 177-202

Published: 2017

e-Print:

1309.4721 [hep-th]

DOI:

10.1007/978-3-319-59939-7_5

View in:

ADS Abstract Service

reference search254 citations

Citations per year

Abstract: (Springer)

We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf–Witten theory by replacing a finite group by a finite 2-group. The basic field in this TQFT is a 2-connection on a principal 2-bundle. We classify topological actions for such theories as well as loop and surface observables. When the topological action is trivial, the TQFT is related to a Dijkgraaf–Witten theory by electric-magnetic duality, but in general it is distinct.We propose the existence of new phases of matter protected by higher symmetry.

Note:

33 pages, 2 figures. significantly reworked version, with corrected 1-form gauge transformations in the lattice theory, and a lattice description of ground states and global symmetry actions of higher SPT phases in the "group cohomology basis" similar to Chen-Gu-Liu-Wen

79: Mathematical Physics
Symmetries
higher categories
topological phases of matter
field theory: topological
action: topological
group: finite
symmetry: gauge
gauge field theory
lattice

References(19)

Figures(0)

[1]

Topological Gauge Theories and Group Cohomology

- Commun.Math.Phys. 129 (1990) 393
•
DOI:
- 10.1007/BF02096988

[2]

Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories

Sergei Gukov
(
- Caltech
)
,
Anton Kapustin
(
- Caltech
)

e-Print:
- 1307.4793

[3]

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement

Anton Kapustin
(
- Caltech
)
,
Ryan Thorngren
(
- UC, Berkeley
)

- Adv.Theor.Math.Phys. 18 (2014) 5, 1233-1247
•
e-Print:
- 1308.2926
•
DOI:
- 10.4310/ATMP.2014.v18.n5.a4

[4]

Electric-Magnetic Duality of Topological Gauge Theories from Compactification

Ryan Thorngren
(
- UC, Berkeley, Math. Dept.
)

e-Print:
- 1309.1489

[5]

Lectures on axiomatic topological quantum field theory

F. Quinn
(
- Virginia Tech.
)

- ,
- In *Park City 1991, Geometry and quantum field theory* 325-453

[6]

Topological Quantum Field Theories from Compact Lie Groups

Daniel S. Freed
(
- Texas U., Math Dept.
)
,
Michael J. Hopkins
(
- Harvard U., Dept. Math.
)
,
Jacob Lurie
(
- MIT
)
,
Constantin Teleman
(
- UC, Berkeley, Math. Dept.
)

e-Print:
- 0905.0731

[7]

Symmetry protected topological orders and the group cohomology of their symmetry group

Xie Chen
(
- MIT, LNS and
- UC, Berkeley (main)
)
,
Zheng-Cheng Gu
(
- Caltech
)
,
Zheng-Xin Liu
(
- Tsinghua U., Beijing and
- MIT, LNS
)
,
Xiao-Gang Wen
(
- MIT, LNS and
- Tsinghua U., Beijing and
- Perimeter Inst. Theor. Phys.
)

- Phys.Rev.B 87 (2013) 15, 155114
•
e-Print:
- 1106.4772
•
DOI:
- 10.1103/PhysRevB.87.155114

[8]

Braiding statistics approach to symmetry-protected topological phases

Michael Levin
(
- Maryland U.
)
,
Zheng-Cheng Gu
(
- Santa Barbara, KITP
)

- Phys.Rev.B 86 (2012) 115109
•
e-Print:
- 1202.3120
•
DOI:
- 10.1103/PhysRevB.86.115109

[9]

Quantized topological terms in weakly coupled gauge theories and their connection to symmetry protected topological phases

Ling-Yan Hung
(
- Perimeter Inst. Theor. Phys. and
- Harvard U., Phys. Dept.
)
,
Xiao-Gang Wen
(
- Perimeter Inst. Theor. Phys. and
- MIT, LNS and
- Tsinghua U., Beijing
)

e-Print:
- 1211.2767

[10]

(3+1)-TQFTs and Topological Insulators

•
e-Print:
- 1104.2632

[11]

Three-dimensional topological lattice models with surface anyons

- Phys.Rev.B 87 (2013) 4, 045107
•
e-Print:
- 1208.5128
•
DOI:
- 10.1103/PhysRevB.87.045107

[12]

Higher-Dimensional Algebra V: 2-Groups

e-Print:
- math/0307200

[13]

Algebraic Topology

A. Hatcher

[14]

Cohomology of groups

K. Brown

[15]

Higher gauge theory: 2-connections on 2-bundles

John Baez
(
- UC, Riverside, Math. Dept.
)
,
Urs Schreiber
(
- Essen U.
)

e-Print:
- hep-th/0412325

[16]

Connections on non-abelian Gerbes and their Holonomy

e-Print:
- 0808.1923

[17]

Quantum Field Theory and the Jones Polynomial

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Commun.Math.Phys. 121 (1989) 351-399,
•
DOI:
- 10.1007/BF01217730

[18]

Reading between the lines of four-dimensional gauge theories

Ofer Aharony
(
- Weizmann Inst. and
- Princeton, Inst. Advanced Study
)
,
Nathan Seiberg
(
- Princeton, Inst. Advanced Study
)
,
Yuji Tachikawa
(
- Tokyo U. and
- Tokyo U., IPMU
)

- JHEP 08 (2013) 115
•
e-Print:
- 1305.0318
•
DOI:
- 10.1007/JHEP08(2013)115

[19]

On the groups H(Π, n). II. Methods of computation

S. Eilenberg
,
S. MacLane