Manifolds Of G2 Holonomy Research Articles

COMPACTIFIED STRING THEORIES — GENERIC PREDICTIONS FOR PARTICLE PHYSICS

In recent years it has been realized that in string/M theories compactified to four dimensions which satisfy cosmological constraints, it is possible to make some generic predictions for particle physics and dark matter: a nonthermal cosmological history before primordial nucleosynthesis, a scale of supersymmetry breaking which is "high" as in gravity mediation, scalar superpartners too heavy to be produced at the LHC (although gluino production is expected in many cases), and a significant fraction of dark matter in the form of axions. When the matter and gauge spectrum below the compactification scale is that of the MSSM, a robust prediction of about 125 GeV for the Higgs boson mass, predictions for various aspects of dark matter physics, as well as predictions for future precision measurements, can be made. As a prototypical example, M theory compactified on a manifold of G2holonomy leads to a good candidate for our "string vacuum," with the TeV scale emerging from the Planck scale, a de Sitter vacuum, robust electroweak symmetry breaking, and solutions of the weak and strong CP problems. In this article we review how these and other results were derived, from the key theoretical ideas to the final phenomenological predictions.

Gravity duals of 2d supersymmetric gauge theories

We find new supergravity solutions generated by D5-branes wrapping a four- cycle and preserving four and two supersymmetries. We first consider the configuration in which the fivebranes wrap a four-cycle in a Calabi-Yau threefold, which preserves four supersymmetries and is a gravity dual to the Coulomb branch of two-dimensional gauge theories with N = (2,2) supersymmetry. We also study the case of fivebranes wrapping a co-associative four-cycle in a manifold of G2-holonomy, which provides a gravity dual of N = (1,1) supersymmetric Yang-Mills theory in two dimensions. We also discuss the addition of unquenched fundamental matter fields to these backgrounds and find the cor- responding gravity solutions with flavor brane sources.

The Topological G<sub>2</sub> String

We construct new topological theories related to sigma models whose target space is a seven-dimensional manifold of G2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six-dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. We also present evidence that one can extend this definition to all genera and construct a seven-dimensional topological string theory. We compute genus zero correlation functions and relate these to Hitchin’s functional for three-forms in seven dimensions. Along the way we develop the analogue of special geometry for G2 manifolds. When the seven-dimensional topological twist is applied to the product of a Calabi–Yau manifold and a circle, the result is an interesting combination of the six-dimensional A and B models.

AdS spacetimes in M‐theory

AbstractWe review recent progress in the classification and construction of supersymmetric AdS solutions of M‐theory. The AdS supersymmetry conditions are derived by taking the near‐horizon limit of M‐fivebranes wrapping supersymmetric cycles in manifolds of G2 or SU(N) holonomy, N = 2, 3, 4. The new explicit solutions we find are AdS3 solutions arising in the near‐horizon limit of M‐fivebranes wrapping Kähler four‐cycles in Calabi‐Yau four‐folds, intersecting membranes in a string, and dual to 𝒩 = (2,0) conformal field theories in two dimensions. Eight doubly countably infinite families of these solutions are reduced and dualised to IIB, and the central charge of the dual field theories computed. Some future directions are briefly discussed.

MTheory Solution to the Hierarchy Problem

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2 holonomy without fluxes. This gives stable vacua with softly broken supersymmetry, grand unification, and a distinctive spectrum of TeV and sub-TeV sparticle masses.

Rotating strings and D2-branes in type IIA reduction of M-theory onG2manifold and their semiclassical limits

We consider rotating strings and D2-branes on type IIA background, which arises as dimensional reduction of M-theory on manifold of G2 holonomy, dual to = 1 gauge theory in four dimensions. We obtain exact solutions and explicit expressions for the conserved charges. By taking the semiclassical limit, we show that the rotating strings can reproduce only one type of semiclassical behavior, exhibited by rotating M2-branes on G2 manifolds. Our further investigation leads to the conclusion that the rotating D2-branes reproduce two types of the semiclassical energy-charge relations known for membranes in eleven dimensions.

Generalized holonomy in String-corrected Spacetimes

The quartic-curvature corrections derived from string theory have a specific impact on the geometry of target-space manifolds of special holonomy. In the cases of Calabi-Yau manifolds, D = 7 manifolds of G2 holonomy and D = 8 manifolds of Spin7 holonomy, string theory α′ corrections conspire to preserve the unbroken supersymmetry of these backgrounds despite the fact that the α′ corrections cause the Riemannian holonomy to lose its special character. We show how this supersymmetry preservation is expressed in the language of generalized holonomy for the Killing spinor operator.

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.

Domain walls, Hitchin's flow equations and G2-manifolds

We construct BPS domain-wall solutions of the effective action of type-IIA string theory compactified on a half-flat six-manifold. The flow equations for the vector and hypermultiplet scalars are shown to be equivalent to Hitchin's flow equations, implying that our domain walls can be lifted to solutions of ten-dimensional type-IIA supergravity. They take the form R1,2 × Y7, where Y7 is a G2-holonomy manifold with boundaries.

Special‐holonomy manifolds and quartic‐curvature string corrections

AbstractThe quartic‐curvature corrections derived from string theory have a very specific impact on the geometry of target‐space manifolds of special holonomy. In the cases of Calabi‐Yau manifolds and D = 7 manifolds of G2 holonomy, we show how the corrections conspire to preserve the unbroken supersymmetry of these backgrounds.

SUPERPOTENTIAL OF THE M-THEORY CONIFOLD AND TYPE IIA STRING THEORY

The membrane instanton superpotential for M-theory on the G2 holonomy manifold given by the cone on S3×S3 is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

FOUR LECTURES ON THE GAUGE/GRAVITY CORRESPONDENCE

We review in a pedagogical manner some of the efforts aimed at extending the gauge/gravity correspondence to nonconformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific examples: fractional D-branes on orbifolds and D-branes wrapped on supersymmetric cycles of Calabi–Yau spaces. We explore in particular which gauge theory information can be extracted from the corresponding supergravity solutions, and what the remaining open problems are. We also briefly explain the connection between these and other approaches, such as fractional branes on conifolds, branes suspended between branes, M5-branes on Riemann surfaces and M-theory on G2-holonomy manifolds, and discuss the role played by geometric transitions in all that.

Conifold transitions and five-brane condensation in M-theory on Spin(7) manifolds

We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a ℂP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond–Ramond flux. This is the first non-trivial example of a topology-changing transition with only 1/16 supersymmetry.

Brane solitons for G2 structures in eleven-dimensional supergravity revisited

We investigate the four-dimensional supergravity theory obtained from the compactification of eleven-dimensional supergravity on a smooth manifold of G2 holonomy. We give a new derivation for the Kähler potential associated with the scalar kinetic term of the N = 1 four-dimensional theory. We then examine some solutions of the four-dimensional theory which arise from wrapped M-branes.

M theory, G2-manifolds and four-dimensional physics

M theory on a manifold of G2-holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and \U0001d4a9 = 1 supersymmetry. In order to obtain, within this framework, the standard features of particle physics, namely non-Abelian gauge groups and chiral fermions, we consider G2-manifolds with certain kinds of singularities at which these features reside. The aim of this paper is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement, receive relatively simple explanations within the context of M theory. We conclude with a brief discussion of the particle physics features of these vacua of M theory.

Disk Instantons, Mirror Symmetry and the Duality Web

Abstract We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also discover an integer IR ambiguity needed to define the quantum theory of D-branes wrapped over non-compact Lagrangian submanifolds. In the large N dual Chern-Simons theory, this ambiguity is mapped to the UV choice of the framing of the knot. In a type IIB dual description involving (p; q) 5-branes, disk instantons of type IIA get mapped to (p; q) string instantons. The M-theory lift of these results lead to computation of superpotential terms generated by M2 brane instantons wrapped over 3-cycles of certain manifolds of G2 holonomy.

RETRACTED: Cohomogeneity One Manifolds of Spin(7) and G2 Holonomy

This article has been retracted at the request of the authors.Reason: Because of an inadvertent mix-up on their part, the article was submitted to, and accepted by, both Annals of Physics and Physical Review D simultaneously. This withdrawal does not in any way reflect on the scientific merit of the work.

Comments on M theory dynamics onG2holonomy manifolds

We study the dynamics of M-theory on G2 holonomy manifolds, and consider in detail the manifolds realized as the quotient of the spin bundle over S^3 by discrete groups. We analyse, in particular, the class of quotients where the triality symmetry is broken. We study the structure of the moduli space, construct its defining equations and show that three different types of classical geometries are interpolated smoothly. We derive the N=1 superpotentials of M-theory on the quotients and comment on the membrane instanton physics. Finally, we turn on Wilson lines that break gauge symmetry and discuss some of the implications.

M-theory conifolds.

Seven manifolds of G2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six manifolds. We find first-order equations for a new family of G2 metrics D7, with S3 x S3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D7 metrics' nontrivial parameter characterizes the squashing of an S3 bolt, which limits to S2 at weak coupling. In general the D7 metrics are asymptotically locally conical, with a nowhere-singular circle action.

Disk Instantons, Mirror Symmetry and the Duality Web

We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also discover an integer IR ambiguity needed to define the quantum theory of D-branes wrapped over non-compact Lagrangian submanifolds. In the large N dual Chern-Simons theory, this ambiguity is mapped to the UV choice of the framing of the knot. In a type IIB dual description involving (p; q) 5-branes, disk instantons of type IIA get mapped to (p; q) string instantons. The M-theory lift of these results lead to computation of superpotential terms generated by M2 brane instantons wrapped over 3-cycles of certain manifolds of G2 holonomy