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We establish a quantitative relationship between mixed de Rham classes and the geometric complexity of metric connections with totally skew torsion on product manifolds where both factors are compact oriented surfaces. For any…
We study a $U(N)$-invariant vector+matrix chain with the color structure of a lattice gauge theory with quarks and interpret it as a theory of open andclosed strings with target space $\Z$. The string field theory is constructed as a…
Nonperturbative corrections in type II string theory corresponding to Riemann surfaces with one boundary are calculated in several noncompact geometries of desingularized orbifolds. One of these models has a complicated phase structure…
We perform the consistent quantization of open string D-brane in non-constant NS-NS closed string B field background by directly imposing the worldsheet conformal symmetry. In addition to the previous noncommutative D-brane coordinates…
A product state of a composite quantum system AB is customarily interpreted physically to mean subsystem A has property A1 and subsystem B has property B1. But this interpretation contradicts both the theory and observed outcomes of…
In this paper we study the string topology (\'a la Chas-Sullivan) of an orbifold. We define the string homology ring product at the level of the free loop space of the classifying space of an orbifold. We study its properties (introducing…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On-shell it is consistent with lightcone quantization, while off-shell it gives a noncommutative superspace that realizes non-linearly a hidden…
In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean…
This contribution gives in sigma-model language a short review of recent work on T-duality for open strings in the presence of abelian or non-abelian gauge fields. Furthermore, it adds a critical discussion of the relation between RG…
Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be vertices. An earlier paper proved the (nonintuitive) result that, conditioned on the event that there is no open path from s to t, the two…
We compute a class of gauge invariant observables for marginal solutions and the tachyon vacuum. In each case we find that the observables are related in a simple way to the closed-string tadpole on a disk with appropriate boundary…
Boundary interactions of closed-string with open-strings are examined intended to provide a constructive formulation of boundary string field theory. As an illustration, we consider the BPS $D$-brane of the type II superstring in a constant…
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under…
We derive the exact form of the spectral interaction of two strings mediated by a constant scalar field using methods derived from noncommutative geometry. This is achieved by considering a non-product modification of the Connes-Lott model…
The problem of an open string in background $B$-field is discussed. Using the discretized model in details we show that the system is influenced by infinite number of second class constraints. We interpret the allowed Fourier modes as the…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
Recent advances in non-critical string theory allow a unique continuation of critical Polyakov string amplitudes to off-shell momenta, while preserving conformal invariance. These continuations possess unusual, apparently stringy,…
In this paper we consider a class of exactly solvable closed string flux backgrounds that exhibit non-commutativity in the closed string coordinates. They are realized in terms of freely-acting asymmetric Z_N-orbifolds, which are themselves…
Several recent papers discuss gravitational corrections to gauge couplings that depend quadratically on the energy. In the framework of the background-field approach, these correspond in general to adding to the effective action terms…