A New Gauge/Gravity Dictionary via the Division Algebras
File(s)
Author(s)
Nagy, Silvia
Type
Thesis
Abstract
The main goal of this thesis is to explore the idea of gravity as the square of a gauge theory
at the level of Lagrangian symmetries. By regarding gravity as the convolution of left and right
Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in
linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance,
local Lorentz invariance and local supersymmetry from the
at space Yang-Mills symmetries of local
gauge invariance and global super-Poincare. As an example, we will we focus on the new-minimal
(12 + 12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell
Yang-Mills multiplets (4 + 4;N_L = 1) and (3 + 0;N_R = 0).
By tensoring all possible pairs of on-shell super Yang-Mills multiplets in dimensions 3 ≤ D ≤ 10 to
get on-shell supergravity multiplets, possibly with additional matter multiplets. By associating a (direct
sum of) division algebra(s) D with each dimension 3 ≤ D ≤ 10 we obtain a formula for the supergravity
U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras
of each super Yang-Mills theory. We then extend our analysis to include supergravities coupled to
an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor
product.
We also introduce the idea of writing the SYM multiplets themselves as a double copy. We construct
the states and symmetries of N = 4 super-Yang-Mills by tensoring two N = 1 chiral multiplets and
introducing two extra SUSY generators. This allows us to write the maximal N = 8 supergravity as four
copies of the chiral multiplet. We extend this to higher dimensions and discuss possible applications.
at the level of Lagrangian symmetries. By regarding gravity as the convolution of left and right
Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in
linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance,
local Lorentz invariance and local supersymmetry from the
at space Yang-Mills symmetries of local
gauge invariance and global super-Poincare. As an example, we will we focus on the new-minimal
(12 + 12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell
Yang-Mills multiplets (4 + 4;N_L = 1) and (3 + 0;N_R = 0).
By tensoring all possible pairs of on-shell super Yang-Mills multiplets in dimensions 3 ≤ D ≤ 10 to
get on-shell supergravity multiplets, possibly with additional matter multiplets. By associating a (direct
sum of) division algebra(s) D with each dimension 3 ≤ D ≤ 10 we obtain a formula for the supergravity
U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras
of each super Yang-Mills theory. We then extend our analysis to include supergravities coupled to
an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor
product.
We also introduce the idea of writing the SYM multiplets themselves as a double copy. We construct
the states and symmetries of N = 4 super-Yang-Mills by tensoring two N = 1 chiral multiplets and
introducing two extra SUSY generators. This allows us to write the maximal N = 8 supergravity as four
copies of the chiral multiplet. We extend this to higher dimensions and discuss possible applications.
Version
Open Access
Date Issued
2015-05
Date Awarded
2015-07
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Duff, Michael
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)