Narrow Results

It is shown that besides the standard real algebraic framework for M-theory a consistent octonionic realization can be introduced. The octonionic M-superalgebra and superconformal M-algebra are derived. The first one involves 52 real bosonic generators and presents a novel and surprising feature, its octonionic M5 (super-5-brane) sector coincides with the M1 and M2 sectors. The octonionic superconformal M-algebra is given by OS_p(1,8∣O) and admits 239 bosonic and 64 fermionic generators.

It is shown that the twisted sector spectrum, as well as the associated Chern–Simons interactions, can be determined on M-theory orbifold fixed planes that do not admit gravitational anomalies. This is demonstrated for the seven-planes arising within the context of an explicit R⁶ × S¹/Z₂ × T⁴/Z₂ orbifold, although the results are completely general. Local anomaly cancellation in this context is shown to require fractional anomaly data that can only arise from a twisted sector on the seven-planes, thus determining the twisted spectrum up to a small ambiguity. These results open the door to the construction of arbitrary M-theory orbifolds, including those containing fixed four-planes which are of phenomenological interest.

We analyze the structure of heterotic M-theory on K3 orbifolds by presenting a comprehensive sequence of M-theoretic models constructed on the basis of local anomaly cancellation. This is facilitated by extending the technology developed in our previous papers to allow one to determine "twisted" sector states in nonprime orbifolds. These methods should naturally generalize to four-dimensional models, which are of potential phenomenological interest.

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.

We outline a brief description of noncommutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.

Diaconescu, Moore and Witten proved that the partition function of type IIA string theory coincides (to the extent checked) with the partition function of M-theory. One of us (Kriz) and Sati proposed in a previous paper a refinement of the IIA partition function using elliptic cohomology and conjectured that it coincides with a partition function coming from F-theory. In this paper, we define the geometric term of the F-theoretical effective action on type IIA compactifications. In the special case when the first Pontrjagin class of space–time vanishes, we also prove a version of the Kriz–Sati conjecture by extending the arguments of Diaconescu–Moore–Witten. We also briefly discuss why even this special case allows interesting examples.

We review our recent proposal for a background-independent formulation of a holographic theory of quantum gravity. The present paper incorporates the necessary background material on geometry of canonical quantum theory, holography and space–time thermodynamics, Matrix theory, as well as our specific proposal for a dynamical theory of geometric quantum mechanics, as applied to Matrix theory. At the heart of this review is a new analysis of the conceptual problem of time and the closely related and phenomenologically relevant problem of vacuum energy in quantum gravity. We also present a discussion of some observational implications of this new viewpoint on the problem of vacuum energy.

We address the question of determining the prepotential of the gauged supergravity resulting from a compactification of M-theory on AdS₄ × Y₇. We make a concrete proposal for the prepotential in the case of toric Sasaki-Einstein Y₇. Comparison with direct Kaluza-Klein computations show that the proposal is correct in certain cases, but requires modification in general.

We continue our study of BPS equations and supersymmetric configurations in the Bagger–Lambert (BL) theory. The superalgebra allows three different types of central extensions which correspond to compounds of various M-theory objects: M2-branes, M5-branes, gravity waves and Kaluza–Klein monopoles which intersect or have overlaps with the M2-branes whose dynamics is given by the BL action. As elementary objects they are all 1/2-BPS, and multiple intersections of n-branes generically break the supersymmetry into 1/2ⁿ, as it is well known. But a particular composite of M-branes can preserve from 1/16 up to 3/4 of the original supersymmetries as previously discovered. In this paper we provide the M-theory interpretation for various BPS equations, and also present explicit solutions to some 1/2-BPS equations.

We give a brief summary of the recently constructed superconformal Chern-Simons-matter theories and and how they describe the dynamics of M2-branes at orbifolds.

We propose the bosonic part of an action that defines M-theory. It possesses manifest SO(1, 10) symmetry and constructed based on the Lorentzian 3-algebra associated with U(N) Lie algebra. From our action, we derive the bosonic sector of BFSS matrix theory and IIB matrix model in the naive large N limit by taking appropriate vacua. We also discuss an interaction with fermions.

The study of AdS/CFT (or gauge/gravity) duality has been one of the most active and illuminating areas of research in string theory over the past decade. The scope of its relevance and the insights it is providing seem to be ever expanding. In this talk I briefly describe some of the attempts to explore how the duality works for maximally supersymmetric systems.

The first lecture gives a colloquium-level overview of string theory and M-theory. The second lecture surveys various attempts to construct a viable model of particle physics. A recently proposed approach, based on F-theory, is emphasized.

We study several types of classical rotating membrane solutions in AdS₄ ×Q^{1, 1, 1} and discuss their field theory duals. Q^{1, 1, 1} is a seven-dimensional Sasaki–Einstein manifold given as a nontrivial U(1) fibration over S²×S²×S², equipped with SU(2)³ ×U(1) isometry. It is recently suggested that there exist quiver Chern–Simons theories which are dual to M-theory in certain orbifolds of Q^{1, 1, 1}. The membrane solutions we consider have in general nonvanishing angular momenta both in AdS₄ and Q^{1, 1, 1} spaces. We present solutions for folded and wrapped membranes. According to the AdS/CFT correspondence, such classical solutions are dual to long operators of the dual conformal field theories in the large coupling limit. We analyze the asymptotic behaviour of the dispersion relation between energy (conformal dimension) and angular momenta (global charges).

In this paper we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with string structure and give three observations. First, that on string manifolds there is no E₈ × E₈ global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory partition function of Diaconescu–Moore–Witten extends from the spin case to the string case. Third, that the cubic refinement law of Diaconescu–Freed–Moore for the phase of the M-theory partition function extends to string manifolds. The analysis relies on extending from invariants which depend on the spin structure to invariants which instead depend on the string structure. Along the way, the one-loop term is refined via the Witten genus.

We present analytic solutions for membrane metric function based on transverse k-center instanton geometries. The membrane metric functions depend on more than two transverse coordinates and the solutions provide realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections. All solutions have partial preserved supersymmetries.

We extend the BFSS matrix theory by means of Lie 3-algebra. The extended model possesses the same supersymmetry as the original BFSS matrix theory, and thus as the infinite momentum frame limit of M-theory. We study dynamics of the model by choosing the minimal Lie 3-algebra that includes u(N) algebra. We can solve a constraint in the minimal model and obtain two phases. In one phase, the model reduces to the original matrix model. In another phase, it reduces to a simple supersymmetric model.

We study two M5-branes on $A_1$ ALE space. We introduce some M2-branes suspended between the M5-branes. Then, the boundaries of M2-branes look like strings. We call them “M-strings.” The M-strings have ${𝒩}=(4,0)$ supersymmetry by considering the brane configuration on $A_1$ ALE space. We calculate the partition function of M-strings by using the refined topological vertex formalism. We find that the supersymmetry of M-strings gets enhanced to ${𝒩}=(4,4)$ by tuning some Kähler parameters. Furthermore, we discuss another possibility of the enhancement of supersymmetry which is different from the above one.

Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac–Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the $E_{11}$ Kac–Moody algebra that was shown recently${}^{1-5}$ to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside $E_{11}$, so that, by constructing the current algebra of $E_{11}$, I obtain both internal gauge theory and gravity theory. The energy–momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein–Hilbert action.

In this paper, we will first derive the Wheeler–DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler–DeWitt equation for the generalized geometry. We analyze such a deformed Wheeler–DeWitt equation in the minisuperspace approximation, and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time reparametrization invariance.