Nonperturbative terms in the free energy of Chern-Simons gauge theory play a key role in its duality to the closed topological string. We show that these terms are reproduced by performing a double scaling limit near the point where the perturbation expansion diverges. This leads to a derivation of closed string theory from this large-N gauge theory along the lines of noncritical string theorie...

O(N) invariant vector models have been shown to possess non-trivial scaling large N limits, at least perturbatively within the loop expansion, a property they share with matrix models of 2D quantum gravity. In contrast with matrix models, however, vector models can be solved in arbitrary dimensions. We present here the analysis of field theory vector models in d dimensions and discuss the natur...

The automorphism groups of the 27 lines on the smooth cubic surface or the 28 bitangents to the general quartic plane curve are well-known to be closely related to the Weyl groups of E6 and E7. We show how classical subconfigurations of lines, such as double-sixes, triple systems or Steiner sets, are easily constructed from certain models of the exceptional Lie algebras. For e7 and e8 we are le...

We analyse the interaction between the lack of credibility (or uncertainty) regarding central bank’s inflation target and central bank’s stabilisation policy. We consider a model in which private sector is uncertain about the bank’s inflation target and update its beliefs on it. Furthermore, we assume that the bank cannot observe the private-sector belief about the inflation target as well as f...

In this paper we present and evaluate a general framework for the design of truthful auctions for matching agents in a dynamic, two-sided market. A single commodity, such as a resource or a task, is bought and sold by multiple buyers and sellers that arrive and depart over time. Our algorithm, Chain, provides the first framework that allows a truthful dynamic double auction (DA) to be construct...

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an im...

The Small Cycle Double Cover Conjectnre, due to J .A. Bondy, states that every simple bridgeless graph on n vertices has a cycle double cover with at most (n 1) cycles. There are a number of classes of graphs for which this conjecture is known to hold; for example, triangulations of surfaces, complete graphs, and 4-connected planar graphs. In this article, we prove that the conjecture holds for...

We examine the two-dimensional U(N) Yang-Mills theory by using the technique of random partitions. We show that the large N limit of the partition function of the 2D Yang-Mills theory on S reproduces the instanton counting of 4D N = 2 supersymmetric gauge theories introduced by Nekrasov. We also discuss that we can take the “double scaling limit” by fixing the product of the N and cell size in ...

I show that the potential V (x,m) = [b 4 −m(1−m)a(a+ 1) ] sn(x,m) dn(x,m) − b(a+ 1 2 ) cn(x,m) dn(x,m) constitutes an unusual QES band-structure problem in one dimension. In particular, I show that for any positive integral or half-integral a, 2a+ 1 band edge eigenvalues and eigenfunctions can be obtained analytically. However, the associated orthogonal polynomials satisfy fourterm (rather than...

We construct an N = 1 theory with gauge group U(nN) and degree n + 1 tree level superpotential whose matrix model spectral curve develops an Argyres-Douglas singularity. The calculation of the tension of domain walls in the U(nN) theory shows that the standard large N expansion breaks down at the Argyres-Douglas points, with tension that scales as a fractional power of N . Nevertheless, it is p...