Generalised Geometry of Supergravity

We reformulate type II supergravity and dimensional restrictions of eleven-dimensionalsupergravity as generalised geometrical analogues of Einsteingravity. The bosonic symmetries are generated by generalised vectors, whilethe bosonic fields are unified into a generalised metric. The generalised tangentspace features a natural action of the relevant (continuous) dualitygroup. Also, the analogues of orthonormal frames for the generalised metricare related by the well-known enhanced local symmetry groups, whichprovide the analogue of the local Lorentz symmetry in general relativity.Generalised connections and torsion feature prominently in the construction,and we show that the analogue of the Levi-Civita connection is notuniquely determined by metric compatibility and vanishing torsion. However,connections of this type can be used to extract the derivative operatorswhich appear in the supergravity equations, and the undetermined piecesof the connection cancel out from these, leaving the required unique expressions.We find that the bosonic action and equations of motion can be interpretedas generalised curvatures, while the derivative operators appearingin the supersymmetry variations and equations of motion for the fermionsbecome very simple expressions in terms of the generalised connection.In the final chapter, the construction is used to reformulate supersymmetricflux backgrounds as torsion-free generalised G-structures. This isthe direct analogue of the special holonomy condition which arises for supersymmetricbackgrounds without flux in ordinary Riemannian geometry.

operator: derivative
symmetry: Lorentz
flux: background
gauge field theory: boson
dimension: 11
supergravity: Type II
torsion
differential geometry
thesis

References(205)

Figures(0)

[1]

Supergravity as Generalised Geometry I: Type II Theories

- JHEP 11 (2011) 091
•
e-Print:
- 1107.1733
•
DOI:
- 10.1007/JHEP11(2011)091

[2]

$E_{d(d)} \times \mathbb{R}^+$ generalised geometry, connections and M theory

- JHEP 02 (2014) 054
•
e-Print:
- 1112.3989
•
DOI:
- 10.1007/JHEP02(2014)054

[3]

Supergravity as Generalised Geometry II: Ed(d) × R+ and M theory

A. Coimbra
,
C. Strickland-Constable
,
D. Waldram

[4]

Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories

G. Veneziano
(
- CERN
)

- Nuovo Cim.A 57 (1968) 190-197
•
DOI:
- 10.1007/BF02824451

[5]

SUPERSTRING THEORY. VOL. 1: INTRODUCTION

M.B. Green
,
J.H. Schwarz
,
E. Witten

[6]

SUPERSTRING THEORY. VOL. 2: LOOP AMPLITUDES, ANOMALIES AND PHENOMENOLOGY

M.B. Green
,
J.H. Schwarz
,
E. Witten

[7]

String theory. Vol. 1: An introduction to the bosonic string

J. Polchinski

[8]

String theory. Vol. 2: Superstring theory and beyond

J. Polchinski

[9]

A first course in string theory

B. Zwiebach

[10]

String theory and M-theory: A modern introduction

K. Becker
,
M. Becker
,
J.H. Schwarz

[11]

Strings in Background Fields

Curtis G. Callan, Jr.
(
- Princeton U.
)
,
E.J. Martinec
(
- Princeton U.
)
,
M.J. Perry
(
- Princeton U.
)
,
D. Friedan
(
- Chicago U., EFI and
- Chicago U.
)

- Nucl.Phys.B 262 (1985) 593-609
•
DOI:
- 10.1016/0550-3213(85)90506-1

[12]

Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory

Michael B. Green
(
- Queen Mary, U. of London and
- Caltech
)
,
John H. Schwarz
(
- Caltech
)

- Phys.Lett.B 149 (1984) 117-122,
- In *Schwarz, J.H. (ed.): Superstrings, Vol. 2*, 1007-1012,
- In *Ferrara, S. (ed.): Supersymmetry, Vol. 2*, 1300-1305,
- In *Appelquist, T. (ed.) et al.: Modern Kaluza-Klein theories*, 608-613,
- In *Salam, A. (ed.), Sezgin, E. (ed.): Supergravities in diverse dimensions, vol. 2* 1146-1151,
- In *Bohm, A. et al.: Dynamical groups and spectrum generating algebras, vol. 2* 912-917,
- In *Froggatt, C.D., Nielsen, H.B.: Origin of symmetries* 450-455
•
DOI:
- 10.1016/0370-2693(84)91565-X

[13]

New Connections Between String Theories

- Mod.Phys.Lett.A 4 (1989) 2073-2083
•
DOI:
- 10.1142/S0217732389002331

[14]

Dirichlet Branes and Ramond-Ramond charges

Joseph Polchinski
(
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 75 (1995) 4724-4727
•
e-Print:
- hep-th/9510017
•
DOI:
- 10.1103/PhysRevLett.75.4724

[15]

World sheet approach to heterotic instantons and solitons

Curtis G. Callan, Jr.
(
- Princeton U.
)
,
Jeffrey A. Harvey
(
- Chicago U., EFI
)
,
Andrew Strominger
(
- UC, Santa Barbara
)

- Nucl.Phys.B 359 (1991) 611-634
•
DOI:
- 10.1016/0550-3213(91)90074-8

[16]

The eleven-dimensional supermembrane revisited

P.K. Townsend
(
- Cambridge U.
)
,
P.V. Landshoff

- ,
- Phys.Lett.B 350 (1995) 184-187,
•
e-Print:
- hep-th/9501068
•
DOI:
- 10.1201/9781482268737-25

[17]

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

[18]

Supergravity Theory in 11 Dimensions

E. Cremmer
(
- Ecole Normale Superieure
)
,
B. Julia
(
- Ecole Normale Superieure
)
,
Joel Scherk
(
- Ecole Normale Superieure
)

- ,
- Phys.Lett.B 76 (1978) 409-412,
- IN *APPELQUIST, T. (ED.) ET AL.: MODERN KALUZA-KLEIN THEORIES*, 202-205. (PHYS. LETT. B76 (1978) 409-412) AND PARIS EC. NORM. SUP. - LPTENS 78-10 (78,REC.MAY) 9 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0370-2693(78)90894-8