Related papers: Branes and integrable lattice models
The theme of this thesis is the study of field theories generically without Lorentz symmetry, but possessing an inhomogeneous scaling symmetry. A number of aspects of such models are explored, including the addition of supersymmetry, and…
I review recent approaches to constructing supersymmetric lattice theories focusing in particular on the concept of topological twisting. The latter technique is shown to expose a nilpotent, scalar supersymmetry which can be implemented…
We study the number of planes for four dimensional projective hypersurfaces which has so-called inductive structure. We also determine transcendental lattices for cubic fourfolds of this type.
We construct a class of intersecting brane solutions with horizon geometries of the form adS_k x S^l x S^m x E^n. We describe how all these solutions are connected through the addition of a wave and/or monopoles. All solutions exhibit…
We solve $\mathcal{N}=1$ supersymmetric $A_{2}$ type $U(N)\times U(N)$ matrix models obtained by deforming $\mathcal{N}=2$ with symmetric tree level superpotentials of any degree exactly in the planar limit. These theories can be…
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact…
This is a review article of my recent papers on free field construction of D-branes in N = 2 superconformal minimal models and Gepner models.
The investigation of strings and M-theory involves the understanding of various BPS solitons which in a certain approximation can be thought of as solutions of ten- and eleven-dimensional supergravity theories. These solitons have a brane…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
We review various aspects of configurations of intersecting branes, including the conditions for preservation of supersymmetry. In particular, we discuss the projection conditions on the Killing spinors for given brane configurations and…
Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this…
It is pointed out that one-component \phi^4 lattice theory in four dimensions has a non-perturbative sector which can be studied by means of an exact duality transformation of its Ising limit. This duality maps it to a membrane model. As a…
We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$ and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
This PhD thesis explores and combines, through the lens of the holographic correspondence, two relevant topics in the field of gravitational high-energy theory: higher-derivative theories of gravity and brane-world models.
$\mathcal{N}=4$ supersymmetric Yang-Mills theories with algebra $\mathfrak{so}(4N)$ and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to the non-invertible…
Synopsis: (i) how superstring theories are unified by M-theory; (ii) how superstring and supermembrane properties follow from the D=10 and D=11 supersymmetry algebras; (iii) how D=10 and D=11 supergravity theories determine the strong…
We construct an N=1 superconformal field theory using branes of type IIA string theory. The IIA construction is related via T-duality to a IIB configuration with 3-branes in a background generated by two intersecting O7-planes and 7-branes.…
This work reports on models described by two real scalar fields coupled with gravity in the five-dimensional spacetime, with a warped geometry involving one infinite extra dimension. Through a mechanism that smoothly changes a thick brane…