Related papers: Knots and Matrix Models
In this short note we would like to show the relation between the cubic string field theory for N D-instantons and the string field theory in the presence of the background B field.
Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagram of a permutation. We show that the permutations which…
We provide a way to produce knots in $S^3$ from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental theorem of finite type invariants. We also provide moves for…
To any integer matrix $A$ one can associate a matroid structure consisting of a graph and another integer matrix $A_B$. The connected components of this graph are called bouquets. We prove that bouquets behave well with respect to the…
We solve the loop equations to all orders in $1/N^2$, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for…
The three-dimensional topologies of the membrane of M-theory can be constructed by performing Dehn surgery along knot lines. We investigate membranes wrapped around a circle and the correponding subset of topologies (Seifert manifolds). The…
High energy fixed angle scattering is studied in matrix string theory. The saddle point world sheet configurations, which give the dominant contributions to the string theory amplitude, are taken as classical backgrounds in matrix string…
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
The representation of knots by petal diagrams (Adams et al. 2012) naturally defines a sequence of distributions on the set of knots. In this article we establish some basic properties of this randomized knot model. We prove that in the…
We discuss aspects of recent novel approaches towards understanding the large N limit of matrix field theories with local or global non-abelian symmetry.
We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
We study consistency conditions on a M(atrix)-model which would describe M-theory on $T^6$. We argue that there is a limit in moduli space for which it becomes a 6+1D theory and study the low-energy description of extended objects in the…
We consider two dimensional supergravity coupled to $\hat c=1$ matter. This system can also be interpreted as noncritical type 0 string theory in a two dimensional target space. After reviewing and extending the traditional descriptions of…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…
We develop new tools for an in-depth study of our recent proposal for Matrix Theory. We construct the anomaly-free and finite planar continuum limit of the ground state with SO(2^{13}) symmetry matching with the tadpole and tachyon free IR…
The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in…
Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed…