Related papers: DLCQ On a Twisted Torus
In tropical geometry, one studies algebraic curves using combinatorial techniques via the tropicalization procedure. The tropicalization depends on a map to an algebraic torus and the combinatorial methods are most useful when the…
In this lecture I will review some results about the discrete light-cone quantization (DLCQ) of strings and some connections of the results with matrix string theory. I will review arguments which show that, in the path integral…
The parameter space of $n$ ordered points in projective $d$-space that lie on a rational normal curve admits a natural compactification by taking the Zariski closure in $(\mathbb{P}^d)^n$. The resulting variety was used to study the…
In this paper we continue our study of the thermodynamics of large N gauge theories on compact spaces. We consider toroidal compactifications of pure SU(N) Yang-Mills theories and of maximally supersymmetric Yang-Mills theories…
The genuine Kaluza-Klein-like theories (with no fields in addition to gravity with torsion) have difficulties with the existence of massless spinors after the compactification of some of dimensions of space\cite{witten}. We demonstrate in…
We study the effect of the topology of universe by gauging the non-relativistic particle model on the torus and 3-torus, using the symplectic formalism of constrained systems and embedding those models on extended phase-spaces. Also, we…
Motivated by recent work on low energy unification, in this short note we derive corrections on Newton's inverse square law due to the existence of extra decompactified dimensions. In the four-dimensional macroscopic limit we find that the…
We point out that the location of renormalon singularities in theory on a circle-compactified spacetime $\mathbb{R}^{d-1} \times S^1$ (with a small radius $R \Lambda \ll 1$) can differ from that on the non-compactified spacetime…
We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can…
We study 2+1D toroidal compactifications of M-theory with twists in the U-duality group. These compactifications realize many symmetric-manifolds from the classification of 2+1D extended supergravity moduli-spaces. We then focus on the…
After a brief review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, we present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus in two…
We study quantum field theory in six dimensions with two of them compactified on a square. A simple boundary condition is the identification of two pairs of adjacent sides of the square such that the values of a field at two identified…
We study (0,2) supersymmetric two-dimensional theories obtained by compactifying four-dimensional N=1 supersymmetric theories on a two-torus, with a magnetic field for a global U(1) symmetry, and present evidence that Seiberg duality in…
We show that in the semi-classical limit the eigenfunctions of quantized ergodic symplectic toral automorphisms can not concentrate in measure on a finite number of closed orbits of the dynamics. More generally, we show that, if the pure…
We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations intersect in the expected dimension. We also…
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted by all commutators between positions, momenta and Hamiltonian…
Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider…
In this paper we study the stochastic quantization problem on the two dimensional torus and establish ergodicity for the solutions. Furthermore, we prove a characterization of the $\Phi^4_2$ quantum field on the torus in terms of its…
This work discusses string compactifications on the torus with optional Z_4 x Z_4 or Z_2 x Z_2 orbifold action from the perspective of matrix factorizations. The method is brought to a level where model building on these backgrounds is…
We consider the torus compactifications with flux of a class of $6d$ $(1,0)$ SCFTs that can be engineered as the low-energy theories on M$5$-branes near an M$9$-plane on a $C^2/Z_2$ singularity. Specifically, we concentrate on the two SCFTs…