This article reviews the matrix model of M theory. theory is an 11-dimensional quantum gravity that believed to underlie all superstring theories. currently most plausible candidate for a fundamental physics which reconciles and field in realistic fashion. Evidence still only circumstantial---no complete background-independent formulation exists as yet. Matrix was first developed regularized supersymmetric membrane. More recently, it has appeared different guise discrete light-cone...

Abstract We classify six-dimensional F-theory compactifications in terms of simple features the divisor structure base surface elliptic fibration. This controls minimal spectrum theory. determine all irreducible configurations divisors (“clusters”) that are required to carry nonabelian gauge group factors based on intersections with one another and canonical class base. All 6D models built from combinations these configurations. Physically, this geometric characterizes algebra matter can...

In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Witten's cubic bosonic open string field theory. We use both low-energy Yang-Mills description and language theory explain problem on unstable D-branes. give self-contained using conformal overlap integrals. Our main subjects are Sen conjectures evidence that supports conjectures. conclude with discussion vacuum projectors star-algebra fields. comment possible role construction nonperturbative...

Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single fourfold ${\cal M}_{\rm max}$ gives rise O} (10^{272,000})$ F-theory flux vacua, and sum total of numbers vacua from all other geometries is suppressed by relative factor (10^{-3000})$. The arises generic fibration over specific toric threefold base $B_{\rm max}$, geometrically non-Higgsable gauge group $E_8^9 \times F_4^8 (G_2 SU(2))^{16}$, which we expect some factors be broken G-flux...

We give a simple description of the classical moduli space vacua for supersymmetric gauge theories with or without superpotential. The key ingredient in our analysis is observation that Lagrangian invariant under action complexified group ${G}^{c}$. From this point view usual $D$-flatness conditions are an artifact Wess-Zumino gauge. By using preserves ${G}^{c}$ invariance we show every constant matter field configuration extremizes superpotential equivalent (in sense make precise) to unique...

We consider membranes of spherical topology in uncompactified Matrix theory.In general for large theory reproduces the classical membrane dynamics up to 1/N corrections; certain simple configurations, equations motion agree exactly at finite N. derive a formula one-loop potential between two finite-sized objects separations.Applied graviton interacting with round membrane, we show that agrees naive supergravity iV, but differs subleading orders The result is quite general: prove pair...

These notes give a pedagogical introduction to D-branes and Matrix theory. The development of the material is based on super Yang-Mills theory, which low-energy field theory describing multiple D-branes. main goal these describe physical properties in language without recourse string methods. This approach motivated by philosophy asserts that all physics light-front M-theory can be described an appropriate

We perform a global analysis of the space consistent 6D quantum gravity theories with N = 1 supersymmetry, including models multiple tensor multiplets. prove that for fewer than T 9 multiplets, finite number distinct gauge groups and matter content are possible. find infinite families field combinations satisfying anomaly cancellation admitting physical kinetic terms > 8. an integral lattice associated each apparently-consistent supergravity theory; this is determined by form polynomial. For...

We show that the N=1 supergravity theories in ten dimensions with gauge groups U(1){496} and E{8}×U(1){248} are not consistent quantum theories. Cancellation of anomalies cannot be made compatible supersymmetry Abelian invariance. Thus, all supersymmetric gravity without known inconsistencies realized string theory.