Generalised geometry methods for supersymmetric compactification moduli with nontrivial flux
File(s)
Author(s)
Smith, George
Type
Thesis
Abstract
We apply the methods of exceptional generalised geometry to compute the infinitesimal
moduli of D = 4 Minkowski compactifications preserving N = 1 supersymmetry, focusing
on the case where the flux represents a nontrivial element in a cohomology group. We
highlight how flux affects the counting of moduli in a collection of examples, in particular
we look at the cases where the moduli are still able to be counted by cohomology groups of
the internal space. We also prove that the cohomology groups counting the infinitesimal
moduli are isomorphic along complex gauge orbits in the space of involutive generalised
SU(7)-structures.
We describe the two “types” of M-theory backgrounds: type 0 and type 3. For type
0, we review how the moduli arise from standard de Rham cohomology classes. For type
3 backgrounds, given a suitable ∂′ ¯∂′-lemma, we show that the moduli can be calculated
from a cohomology based on an involutive sub-bundle of the complexified tangent space.
We then calculate the moduli of heterotic M-theory and show they match those of the
dual Hull–Strominger system, as expected. The rich gauge orbit structure of the space of
SU(7)-structures allows us to argue that the Hull–Strominger moduli receive no corrections
as the string coupling becomes large, making the heterotic M-theory moduli exact to all
loop orders.
We present in detail how conventional structures are embedded within their generalised
counterparts and how conventional conditions emerge from vanishing generalised torsion.
For type II backgrounds with underlying SU(3) structures we derive the most general
conditions the infinitesimal moduli must satisfy. We understand how to interpret these
cohomologically only when the background has the topology of a Calabi-Yau. We also
briefly comment on how these generalised methods can be used to understand fluxed Mirror
symmetry on the backgrounds themselves, rather than in the effective action.
moduli of D = 4 Minkowski compactifications preserving N = 1 supersymmetry, focusing
on the case where the flux represents a nontrivial element in a cohomology group. We
highlight how flux affects the counting of moduli in a collection of examples, in particular
we look at the cases where the moduli are still able to be counted by cohomology groups of
the internal space. We also prove that the cohomology groups counting the infinitesimal
moduli are isomorphic along complex gauge orbits in the space of involutive generalised
SU(7)-structures.
We describe the two “types” of M-theory backgrounds: type 0 and type 3. For type
0, we review how the moduli arise from standard de Rham cohomology classes. For type
3 backgrounds, given a suitable ∂′ ¯∂′-lemma, we show that the moduli can be calculated
from a cohomology based on an involutive sub-bundle of the complexified tangent space.
We then calculate the moduli of heterotic M-theory and show they match those of the
dual Hull–Strominger system, as expected. The rich gauge orbit structure of the space of
SU(7)-structures allows us to argue that the Hull–Strominger moduli receive no corrections
as the string coupling becomes large, making the heterotic M-theory moduli exact to all
loop orders.
We present in detail how conventional structures are embedded within their generalised
counterparts and how conventional conditions emerge from vanishing generalised torsion.
For type II backgrounds with underlying SU(3) structures we derive the most general
conditions the infinitesimal moduli must satisfy. We understand how to interpret these
cohomologically only when the background has the topology of a Calabi-Yau. We also
briefly comment on how these generalised methods can be used to understand fluxed Mirror
symmetry on the backgrounds themselves, rather than in the effective action.
Version
Open Access
Date Issued
2023-05
Date Awarded
2024-04
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Waldram, Daniel
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)