相关论文: Finite representations of a quiver arising from st…
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…
We briefly review a class of four dimensional $\mathcal N=3$ field theories constructed by taking a quotient of $\mathcal N=4$ SYM with gauge group $U(N)$. The quotient involves a discrete symmetry that only exists for specific, order one,…
We formulate the string field theory in zero-dimensional target space corresponding to the two-dimensional quantum gravity theory defined through Causal Dynamical Triangulations. This third quantization of the quantum gravity theory allows…
We investigate strings theories as defined from four dimensional gauge theories. It is argued that novel (super)string theories exist up to 26 dimensions. Some of them may support weakly curved geometries.
We study N=1 four dimensional quiver theories arising on the worldvolume of D3-branes at del Pezzo singularities of Calabi-Yau threefolds. We argue that under local mirror symmetry D3-branes become D6-branes wrapped on a three torus in the…
Given a directed graph E, we construct for each real number l a quiver whose vertex space is the topological realisation of E, and whose edges are directed paths of length l in the vertex space. These quivers are not topological graphs in…
We construct the U(N) spinning particle theories, which describe particles moving on Kahler spaces. These particles have the same relation to the N=2 string as usual spinning particles have to the NSR string. We find the restrictions on the…
In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling…
Some old and new evidence for the existence of the string (planar random surfaces) representation of multicolour QCD are reviewed. They concern the random surface representation of the strong coupling expansion in lattice multicolour gauge…
A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely: the new feature of multistring solutions; the effect of a cosmological constant and of spacial curvature on…
Using a classical action associated to a point-particle in (1+1)-dimensions the classical string theory is derived. In connection with this result two aspects are clarified: First, the point particle in (1+1)-dimensions is not an ordinary…
We have two parallel goals of this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the…
We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
String theory on curved backgrounds has received much attention on account of both its own interest, and of its relation with gauge theories. Despite the progress made in various directions, several quite elementary questions remain…
We construct two new classes of exact solutions to string theory which are not of the standard plane wave or gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution,…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric…
We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…
We study the category $\textrm{Rep}(Q,\mathbb{F}_1)$ of representations of a quiver $Q$ over "the field with one element", denoted by $\mathbb{F}_1$, and the Hall algebra of $\textrm{Rep}(Q,\mathbb{F}_1)$. Representations of $Q$ over…