Related papers: Matrix Factorizations for Local F-Theory Models
We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes…
We realize the CFT with target a lens space SU(2)/Z_l as a simple current construction. This allows us to compute the boundary states and the annuli coefficients, and in particular to study the B-type branes, in purely algebraic terms.…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
We discuss a matrix model for D0-branes on S^3 \times M^7 based on quantum group symmetries. For finite radius of S^3 (i.e. for finite k), it gives results beyond the reach of the ordinary matrix model. For large k all known static…
Representations of small quantum groups $u_q({\mathfrak{g}})$ at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algebra and mathematical physics. There is an ansatz by Lusztig…
We study the exceptional U duality group $E_d$ of M-theory compactified on a d-torus and its representations using Matrix theory. We exhibit the $E_d$ structure and show that p-branes wrapped or unwrapped around the longitudinal direction…
Let $(S,\mathfrak n)$ be a regular local ring and $f$ a non-zero element of $\mathfrak n^2$. A theorem due to Kn\"orrer states that there are finitely many isomorphism classes of maximal Cohen-Macaulay $R=S/(f)$-modules if and only if the…
We derive self-similar string solutions in a graph representation, near the point of singularity formation, which can be shown to extend to point-like singularities on M-branes, as well as to the radially symmetric case.
We study branes and open strings in a large class of orbifolds of a curved background using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex…
Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a…
Solutions corresponding to finite temperature (anti)-D3 and M2 branes localised in flux backgrounds are constructed in a linear approximation. The flux backgrounds considered are toy models for the IR of the Klebanov-Strassler solution and…
We study a particular N = 1 confining gauge theory with fundamental flavors realised as seven branes in the background of wrapped five branes on a rigid two-cycle of a non-trivial global geometry. In parts of the moduli space, the five…
Extra dimensions have been used as attempts to explain several phenomena in particle physics. In this paper we investigate the role of brane-localized kinetic terms (BLKT) on thin and thick branes with two flat extra dimensions (ED)…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
We study D-branes extended in T^2/Z_4 using the mirror description as a tensor product of minimal models. We describe branes in the mirror both as boundary states in minimal models and as matrix factorizations in the corresponding…
In this PhD thesis we discuss methods of recognizing finite groups by the structure of normalizers of certain 3-subgroups. We explain a method for characterizing groups using character theoretic and block theoretic methods and we use these…
Singular limits of 6D F-theory compactifications are often captured by T-branes, namely a non-abelian configuration of intersecting 7-branes with a nilpotent matrix of normal deformations. The long distance approximation of such 7-branes is…
This work deals with the presence of defect structures in models described by real scalar field in a diversity of scenarios. The defect structures which we consider are static solutions of the equations of motion which depend on a single…
The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…