M-theory Vacua Research Articles

Janus on the brane

We present a non-supersymmetric deformation of probe branes describing conformal defects of codimension two in AdS/CFT. The worldvolume of the probe branes is deformed from AdSp× S1 embedded in an AdSp+2× ℳD − p − 2 background to an embedding of Janus form, which uses an AdSp−1 slicing of AdSp and in which the brane bends along the slicing coordinate. In field theory terms this realizes conformal interfaces on codimension- two defects. We discuss these “Janus on the brane” solutions for AdS3× S1 D3-branes in the AdS5× S5 solution of Type IIB, realizing interfaces on surface defects in mathcal{N} = 4 SYM, and show that similar solutions exist for probe branes in AdSp+2× S9−p vacua of M-theory and in the AdS6× S4 solution of massive Type IIA.

3d N = 1 $$ \mathcal{N}=1 $$ effective supergravity and F-theory from M-theory on fourfolds

We consider 3d N=1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions. We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N=1 theory in the large-volume limit up to quartic fermion terms. We show that in general it is an ungauged N=1 supergravity of the form expected from 3d supersymmetry. In particular the massless bosonic fields consist of the volume modulus and the axions originating from the eleven-dimensional three-form, while the moduli-space metric is locally isometric to hyperbolic space. We consider the F-theory interpretation of the 3d N=1 M-theory vacua in the light of the F-theory effective action approach. We show that these vacua generally have F-theory duals with circle fluxes, thus breaking 4d Poincar\'e invariance.

F-theory vacua with [formula omitted] gauge symmetry

Discrete gauge groups naturally arise in F-theory compactifications on genus-one fibered Calabi–Yau manifolds. Such geometries appear in families that are parameterized by the Tate–Shafarevich group of the genus-one fibration. While the F-theory compactification on any element of this family gives rise to the same physics, the corresponding M-theory compactifications on these geometries differ and are obtained by a fluxed circle reduction of the former. In this note, we focus on an element of order three in the Tate–Shafarevich group of the general cubic. We discuss how the different M-theory vacua and the associated discrete gauge groups can be obtained by Higgsing of a pair of five-dimensional U(1) symmetries. The Higgs fields arise from vanishing cycles in I2-fibers that appear at certain codimension two loci in the base. We explicitly identify all three curves that give rise to the corresponding Higgs fields. In this analysis the investigation of different resolved phases of the underlying geometry plays a crucial rôle.

MODELING M-THEORY VACUA VIA GAUGED S-DUALITY

We construct a model of M-theory vacua using gauged S-duality and the Chan–Paton symmetries by introducing an infinite number of open string charges. In the Bechi–Rouet–Stora–Tyutin formalism, the local description of the gauged S-duality on its moduli space of vacua is fully determined by one physical state condition on the vacua. We introduce the string probe of the spatial degrees of freedom and define the increment of the cosmic time. The dimensionality of space–time and the gauge group of the low energy effective theory originate in the symmetries (with or without their breakdown) in our model. This modeling leads to the derived category formulation of the quantum mechanical world including gravity and to the concept of a nonlinear potential of gauged and affinized S-duality which specifies the morphism structure of this derived category.

A simple class of 𝒩 = 3 gauge/gravity duals

We find the gravity duals to an infinite series of N=3 Chern-Simons quiver theories. They are AdS_4 x M_7 vacua of M-theory, with M_7 in a certain class of 3-Sasaki-Einstein manifolds obtained by a quotient construction. The field theories can be engineered from a brane configuration; their geometry is summarized by a hyperKaehler toric fan that can be read off easily from the relative angles of the branes. The singularity at the tip of the cone over M_7 is generically not an orbifold. The simplest new manifolds we consider can be written as the biquotient U(1)\U(3)/U(1). We also comment on the relation between our theories and four-dimensional N=1 theories with the same quiver.

Classification of supersymmetric flux vacua in M-theory

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 particular, we find for N = 2 supersymmetry, that the external space–time is Minkowski and the base manifold of the internal space is conformally Kähler for SU ( 2 ) structures, while for SU ( 3 ) structures the internal space has to be Einstein–Sasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with N = 1 supersymmetry and SU ( 3 ) structure, where all fluxes are non-zero and the first order differential equations are solved.

Features of de Sitter vacua in M-theory

We compute the masses of all moduli in the unstable deSitter vacua arising in the toy model of cosmological M-theory flux compactifications on the G2 holonomy manifolds of [1]. The slow-roll parameters in the tachyonic directions are shown to be too large to be useful for conventional models of inflation. However, it appears that we can find fast roll regimes which could, under certain conditions, account for the current dark energy driven accelerated expansion of the universe.

Regular non-Abelian vacua inN=4,SO(4)gauged supergravity

We present a family of globally regular $\mathcal{N}=1$ vacua in the $\mathrm{D}=4$, $\mathcal{N}=4$ gauged supergravity of Gates and Zwiebach. These solutions are labeled by the ratio $\ensuremath{\xi}$ of the two gauge couplings, and for $\ensuremath{\xi}=0$ they reduce to the supergravity monopole previously used for constructing the gravity dual of $\mathcal{N}=1$ super Yang-Mills theory. For $\ensuremath{\xi}>0$ the solutions are asymptotically anti- de Sitter, but with an excess of the solid angle, and they reduce exactly to anti-de Sitter for $\ensuremath{\xi}=1$. Solutions with $\ensuremath{\xi}<0$ are topologically ${R}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{3}$, and for $\ensuremath{\xi}=\ensuremath{-}2$ they become ${R}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ geometrically. All solutions with $\ensuremath{\xi}\ensuremath{\ne}0$ can be promoted to $\mathrm{D}=11$ to become vacua of M-theory.

Hidden spacetime symmetries and generalized holonomy in M-theory

In M-theory vacua with vanishing 4-form F (4), one can invoke the ordinary Riemannian holonomy H⊂SO(10,1) to account for unbroken supersymmetries n=1, 2, 3, 4, 6, 8, 16, 32. However, the generalized holonomy conjecture, valid for non-zero F (4), can account for more exotic fractions of supersymmetry, in particular 16< n<32. The conjectured holonomies are given by H⊂ G , where G are the generalized structure groups G= SO(d−1,1)×G (spacelike) , G= ISO(d−1)×G (null) and G= SO(d)×G (timelike) with 1⩽ d<11. For example, G(spacelike)=SO(16), G (null)=[ SU(8)× U(1)]⋉ R 56 and G (timelike)= SO ∗(16) when d=3. Although extending spacetime symmetries, there is no conflict with the Coleman–Mandula theorem. The holonomy conjecture rules out certain vacua which are otherwise permitted by the supersymmetry algebra.

Duality symmetric massive type II theories inD= 8 andD= 6

We study $T^2$ compactification of massive type IIA supergravity in presence of possible Ramond-Ramond (RR) background fluxes. The resulting theory in D=8 is shown to possess full $SL(2,R)\times SL(2,R)$ T-duality symmetry similar to the massless case. It is shown that elements of duality symmetry interpolate between massive type IIA compactified on $T^2$ and ordinary type IIA compactified on $T^2$ with RR 2-form flux. We also discuss relationship between M-theory vacua and massive type IIA vacua. The D8-brane is found to correspond to M-theory `pure gravity' solution which is a direct product of 7-dimensional Minkowski space and a 4-dimensional instanton. We also construct D6-D8 bound state which preserves 1/2 supersymmetries. We then discuss massive IIA compactification on $T^4$ and point out that when all possible RR fluxes on $T^4$ are turned on the six-dimensional theory appears to assume a nice SO(4,4) invariant form.

Phenomenology of low quantum gravity scale models

We study some phenomenological implications of models where the scale of quantum gravity effect lies much below the four-dimensional Planck scale. These models arise from M-theory vacua where either the internal space volume is large or the string coupling is very small. We provide a critical analysis of ways to unify electroweak, strong, and gravitational interactions in M theory. We discuss the relations between different scales in two M vacua: type I strings and Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Witten supergravity models. The latter allows possibilities for an 11-dimensional scale at TeV energies with one large dimension below separating our four-dimensional world from a hidden one. Different mechanisms for breaking supersymmetry (gravity mediated, gauge mediated, and Scherk-Schwarz mechanisms) are discussed in this framework. Some phenomenological issues such as dark matter (with masses that may vary in time), origin of neutrino masses, and axion scale are discussed. We suggest that these are indications that the string scale may be lying in the ${10}^{10}--{10}^{14 }$GeV region.

Holomorphic vector bundles and non-perturbative vacua in M-theory

We review the spectral cover formalism for constructing both U(n) and SU(n) holomorphic vector bundles on elliptically fibered Calabi-Yau three-folds which admit a section. We discuss the allowed bases of these three-folds and show that physical constraints eliminate Enriques surfaces from consideration. Relevant properties of the remaining del Pezzo and Hirzebruch surfaces are presented. Restricting the structure group to SU(n), we derive, in detail, a set of rules for the construction of three-family particle physics theories with phenomenologically relevant gauge groups. We show that anomaly cancellation generically requires the existence of non-perturbative vacua containing five-branes. We illustrate these ideas by constructing four explicit three-family non-perturbative vacua.