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DIAS-STP-16-08, Imperial/TP/2016/MJD/02, DFPD/2016/TH-07
Twin Supergravities from Yang-Mills Squared
A. Anastasiou,
1, ∗
L. Borsten,
2, †
M. J. Duff,
3, ‡
M. J. Hughes,
3, §
A. Marrani,
4, 5, ¶
S. Nagy,
6, ∗∗
and M. Zoccali
3, ††
1
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
2
School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland
3
Theoretical Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
4
Centro Studi e Ricerche “Enrico Fermi”, Via Panisperna 89A, I-00184, Roma, Italy
5
Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova,
and INFN, sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
6
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos Pavilhão de
Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa Portugal
(Dated: October 26, 2016)
We consider ‘twin supergravities’ - pairs of supergravities with N
+
and N
−
supersymmetries,
N
+
> N
−
, with identical bosonic sectors - in the context of tensoring super Yang-Mills multiplets.
It is demonstrated that the pairs of twin supergravity theories are related through their left and right
super Yang-Mills factors. This procedure generates new theories from old. In particular, the matter
coupled N
−
twins in D = 3, 5, 6 and the N
−
= 1 twins in D = 4 have not, as far as we are aware, been
obtained previously using the double-copy construction, adding to the growing list of double-copy
constructible theories. The use of fundamental matter multiplets in the double-copy construction
leads us to introduce a bi-fundamental scalar that couples to the well-known bi-adjoint scalar field.
It is also shown that certain matter coupled supergravities admit more than one factorisation into
left and right super Yang-Mills-matter theories.
PACS numbers: 11.30.Pb,11.15.-q,02.20.-a,02.20.-a
Keywords: Yang-Mills theory, supergravity, amplitudes, symmetries
CONTENTS
I. Introduction 2
II. Twin supergravity theories 3
III. Twins from super Yang-Mills squared 6
A. Example: the D = 4, (6, 2) twin theories 11
B. Summary: the pyramid twins in D = 3, 4, 5, 6 15
C. The triplets 21
D. Other twins 23
IV. Conclusions 24
Acknowledgements 24
A. Irreducible Riemannian globally symmetric Kähler and Quaternionic Manifolds 24
B. Bi-adjoint coupled to bi-fundamental scalar theory: a 5-point example 25
References 26
∗
alexandros.anastasiousu@su.se
†
leron@stp.dias.ie
‡
m.duff@imperial.ac.uk
§
mia.hughes07@imperial.ac.uk
¶
alessio.marrani@pd.infn.it
∗∗
snagy@math.tecnico.ulisboa.pt
††
m.zoccali14@imperial.ac.uk
Typeset by REVT
E
X
arXiv:1610.07192v2 [hep-th] 25 Oct 2016
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