# Pauli reductions of supergravities in six and five dimensions

## Abstract

The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, e.g., the S ^{7} reduction of 11-dimensional supergravity, such a consistent “Pauli reduction” does exist. In this paper, we study this existence question in two examples of S ^{2} reductions of supergravities. We do this by making use of a relation between certain S ^{2} reductions and group manifold S ^{3} = S U ( 2 ) reductions of a theory in one dimension higher. By this means, we establish the nonexistence of a consistent S ^{2} Pauli reduction of five-dimensional minimal supergravity. We also show that a previously discovered consistent Pauli reduction of six-dimensional Salam-Sezgin supergravity can be elegantly understood via a group-manifold reduction from seven dimensions.

- Authors:

- Texas A & M Univ., College Station, TX (United States)
- Texas A & M Univ., College Station, TX (United States); Univ. of Cambridge (United Kingdom)

- Publication Date:

- Research Org.:
- Texas A & M Univ., College Station, TX (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1464304

- Alternate Identifier(s):
- OSTI ID: 1498830

- Grant/Contract Number:
- sc0010813; FG02-13ER42020

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
Azizi, Arash, and Pope, C. N. Pauli reductions of supergravities in six and five dimensions. United States: N. p., 2018.
Web. doi:10.1103/physrevd.98.046010.
```

```
Azizi, Arash, & Pope, C. N. Pauli reductions of supergravities in six and five dimensions. United States. doi:10.1103/physrevd.98.046010.
```

```
Azizi, Arash, and Pope, C. N. Mon .
"Pauli reductions of supergravities in six and five dimensions". United States. doi:10.1103/physrevd.98.046010.
```

```
@article{osti_1464304,
```

title = {Pauli reductions of supergravities in six and five dimensions},

author = {Azizi, Arash and Pope, C. N.},

abstractNote = {The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, e.g., the S7 reduction of 11-dimensional supergravity, such a consistent “Pauli reduction” does exist. In this paper, we study this existence question in two examples of S2 reductions of supergravities. We do this by making use of a relation between certain S2 reductions and group manifold S3 = S U ( 2 ) reductions of a theory in one dimension higher. By this means, we establish the nonexistence of a consistent S2 Pauli reduction of five-dimensional minimal supergravity. We also show that a previously discovered consistent Pauli reduction of six-dimensional Salam-Sezgin supergravity can be elegantly understood via a group-manifold reduction from seven dimensions.},

doi = {10.1103/physrevd.98.046010},

journal = {Physical Review D},

number = 4,

volume = 98,

place = {United States},

year = {2018},

month = {8}

}

DOI: 10.1103/physrevd.98.046010

Works referenced in this record:

##
Consistent group and coset reductions of the bosonic string

journal, October 2003

- Cveti, M.; Gibbons, G. W.; Lü, H.
- Classical and Quantum Gravity, Vol. 20, Issue 23

##
SU(2) reduction of six-dimensional (1,0) supergravity

journal, September 2003

- Lü, H.; Pope, C. N.; Sezgin, E.
- Nuclear Physics B, Vol. 668, Issue 1-2

##
Consistent nonlinear KK reduction of 11d supergravity on AdS7×S4 and self-duality in odd dimensions

journal, December 1999

- Nastase, Horatiu; Vaman, Diana; Nieuwenhuizen, Peter van
- Physics Letters B, Vol. 469, Issue 1-4

##
Consistency of the AdS7×S4 reduction and the origin of self-duality in odd dimensions

journal, August 2000

- Nastase, Horatiu; Vaman, Diana; van Nieuwenhuizen, Peter
- Nuclear Physics B, Vol. 581, Issue 1-2

##
The consistency of the S7 truncation in d=11 supergravity

journal, January 1987

- De Wit, B.; Nicolai, H.
- Nuclear Physics B, Vol. 281, Issue 1-2

##
and reductions of type IIA supergravity

journal, December 2000

- Cvetič, M.; Lü, H.; Pope, C. N.
- Nuclear Physics B, Vol. 590, Issue 1-2

##
Chiral compactification on Minkowski × S2 of N = 2 Einstein-Maxwell supergravity in six dimensions

journal, November 1984

- Salam, Abdus; Sezgin, E.
- Physics Letters B, Vol. 147, Issue 1-3

##
Consistent Pauli reduction of six-dimensional chiral gauged Einstein–Maxwell supergravity

journal, October 2004

- Gibbons, G. W.; Pope, C. N.
- Nuclear Physics B, Vol. 697, Issue 1-2

##
Consistent type IIB reductions to maximal 5D supergravity

journal, September 2015

- Baguet, Arnaud; Hohm, Olaf; Samtleben, Henning
- Physical Review D, Vol. 92, Issue 6

##
Consistent Pauli reduction on group manifolds

journal, January 2016

- Baguet, A.; Pope, C. N.; Samtleben, H.
- Physics Letters B, Vol. 752

##
A string and M-theory origin for the Salam–Sezgin model

journal, January 2004

- Cvetič, M.; Gibbons, G. W.; Pope, C. N.
- Nuclear Physics B, Vol. 677, Issue 1-2