arXiv research

Study electric-magnetic duality in M-theory compactifications.

The mathematical features of a string theory compactification determine the physics of the effective four-dimensional theory. For this reason, understanding the mathematical structure of the possible compactification spaces is of profound importance. It is well established that the compactification space for M-Theory m…

We study a particular class of supersymmetric M-theory eight-dimensional non-geometric compactification backgrounds to three-dimensional Minkowski space-time, proving that the global space of the non-geometric compactification is still a differentiable manifold, although with very different geometric and topological pr…

We develop a systematic method for classifying supersymmetric orbifold compactifications of M-theory. By restricting our attention to abelian orbifolds with low order, in the special cases where elements do not include coordinate shifts, we construct a "periodic table" of such compactifications, organized according to …

Motivated by the description of $\mathcal{N}=1$ M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higher-dimensional manifold equipped with a torsion-free structure. As a n…

We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kahler-Atiyah algebra of the compactification space, a description which has wide-ranging applications. As a motivating example, we consider the most general M-theory c…

Y-algebroids generalize symmetry structures for string/M-theory compactifications.

Starting from a higher Courant bracket associated to exceptional generalized geometry, we provide a systematic derivation of all types of fluxes and their Bianchi identities for four-dimensional compactifications of M-theory. We show that these fluxes may be understood as generalized Wess-Zumino terms in certain topolo…

We summarize our geometric and topological description of compact eight-manifolds which arise as internal spaces in ${\cal N}=1$ flux compactifications of M-theory down to $\mathrm{AdS}_3$, under the assumption that the internal part of the supersymmetry generator is everywhere non-chiral. Specifying such a supersymmet…

We show that supersymmetric M-theory compactifications to three-dimensional Minkowski space-time preserving $\mathcal{N}=2$ supersymmetry allow for a class of internal manifolds more general than the Calabi-Yau one, namely the class of locally conformally Kähler manifolds which locally carry a preferred Calabi-Yau stru…

Study 3d N=1 vacua from M-theory compactification on Spin(7) space.

We develop methods to study the singularities of certain $G_2$ cones related to toric hyperkahler spaces and Einstein selfdual orbifolds. This allows us to determine the low energy gauge groups of chiral N=1 compactifications of M-theory on a large family of such backgrounds, which includes the models recently studied …

Study new ECS structures in 5D Minkowski compactifications of M-theory.

We study `constrained generalized Killing (s)pinors', which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constrain…

In 1981, covariantly constant spinors were introduced into Kaluza-Klein theory as a way of counting the number of supersymmetries surviving compactification. These are related to the holonomy group of the compactifying manifold. The first non-trivial example was provided in 1982 by D=11 supergravity on the squashed S7,…

We investigate the local geometry on the moduli space of G_2 structures that arises in compactifications of M-theory on holonomy G_2 manifolds. In particular, we determine the homogeneity properties of couplings of the associated N=1, D=4 supergravity under the scaling of moduli space coordinates. We then find some bra…

We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold $\mat…

We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homtopy equivalence. In the non-simply connected case, which is important for model building, the…

Unified Higgs bundle vacua from M-theory on Spin(7) spaces.

We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits $U(1)^3$ gauge symmetry and a spectrum o…

We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S…

In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with the real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications $SL(2,{\mathbb Z}+i{\mathbb Z})/\{\pm Id\}$…

The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.

We characterize compact eight-manifolds M which arise as internal spaces in N=1 flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equiva…

A longstanding question in superstring/$M$ theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact Ricci flat manifolds have special holonomy in dimensions below eleven. Almost equiva…

Motivated by the quest to understand the analog of non-geometric flux compactification in the context of M-theory, we study higher dimensional analogs of generalized Poisson sigma models and corresponding dual string and p-brane models. We find that higher generalizations of the algebraic structures due to Dorfman, Roy…

M-theory compactified on $G_2$-holonomy manifolds results in 4d $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle…

We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In…

We expand upon a claim made in a recent paper [arXiv:1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak integrability condition in the language of $E_{d(d)}\times\mathbb{R}^+$ generalised geomet…

New mathematical framework connects M-theory charges to stable homotopy groups.

We summarize the foliation approach to ${\cal N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to $\mathrm{AdS}_3$ spaces for the case when the internal part $ξ$ of the supersymmetry generator is chiral on some proper subset ${\cal W}$ of $M$. In this case, a topological no-go theo…

We define intrinsic torsion in generalised geometry and use it to introduce a new notion of generalised special holonomy. We then consider generic warped supersymmetric flux compactifications of M theory and Type II of the form $\mathbb{R}^{D-1,1}\times M$. Using the language of $E_{d(d)}\times\mathbb{R}^+$ generalised…

We show that generalised geometry gives a unified description of bosonic eleven-dimensional supergravity restricted to a $d$-dimensional manifold for all $d\leq7$. The theory is based on an extended tangent space which admits a natural $E_{d(d)} \times \mathbb{R}^+$ action. The bosonic degrees of freedom are unified as…

Extended symmetries and anomalies in compactified 6d SCFTs on various internal manifolds.

We describe a class of compact $G_2$ orbifolds constructed from non-symplectic involutions of K3 surfaces. Within this class, we identify a model for which there are infinitely many associative submanifolds contributing to the effective superpotential of M-theory compactifications. Under a chain of dualities, these can…

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an impor…

Study of exceptional algebroids in type IIA string theory.

The requirement of ${\cal N}=1$ supersymmetry for M-theory backgrounds of the form of a warped product ${\cal M}\times_{w}X$, where $X$ is an eight-manifold and ${\cal M}$ is three-dimensional Minkowski or AdS space, implies the existence of a nowhere-vanishing Majorana spinor $ξ$ on $X$. $ξ$ lifts to a nowhere-vanishi…

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is…

We use the theory of singular foliations to study ${\cal N}=1$ compactifications of eleven-dimensional supergravity on eight-manifolds $M$ down to $\mathrm{AdS}_3$ spaces, allowing for the possibility that the internal part $ξ$ of the supersymmetry generator is chiral on some locus ${\cal W}$ which does not coincide wi…

Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory.…

We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the geometry of backgrounds of key supergravity theories, which have applications in the c…

Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic disc…

We analyse the geometry of generic Minkowski $\mathcal{N}=1$, $D=4$ flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of $\mathrm{G}_2$ holonomy manifolds. In type II theories, they extend the notion of Calabi--Yau ge…

Researchers find new $G_2$-conifolds in $M$-theory with potential field theory duals.

We summarize the global geometric formulation of Einstein-Scalar-Maxwell theories twisted by flat symplectic vector bundle which encodes the duality structure of the theory. We describe the scalar-electromagnetic symmetry group of such models, which consists of flat unbased symplectic automorphisms of the flat symplect…

This thesis is devoted to various questions connected with duality. It is composed of two parts. The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with various signatures (low energy limit of $M$-theories which are dual under timelike T-…

The Bianchi identities for bosonic fluxes in supergravity can receive higher derivative quantum and string corrections, the most well known being that of Heterotic theory $d H = \tfrac{1}{4}α'(\text{tr } F^2 - \text{tr } R^2)$. Less studied are the modifications at order $R^4$ that may arise, for example, in the Bianch…