Related papers: Heterotic Quantum Cohomology
We investigate Hardy spaces $H^1_L(X)$ corresponding to self-adjoint operators $L$. Our main aim is to obtain a description of $H^1_L(X)$ in terms of atomic decompositions similar to such characterisation of the classical Hardy spaces…
We examine how to construct explicit heterotic string models dual to F-theory in eight dimensions. In doing so we learn about where the moduli spaces of the two theories overlap, and how non-perturbative features leave traces on a purely…
We argue that any non-gravitational holographic dual to asymptotically flat string theory in $d$-dimensions naturally resides at spacelike infinity. Since spacelike infinity can be resovled as a $(d-1)$-dimensional timelike hyperboloid…
The flat pp-wave background geometry has been realized as a particular Penrose limit of AdS_5 x S^5. It describes a string that has been infinitely boosted along an equatorial null geodesic in the S^5 subspace. The string worldsheet…
Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -- symplectic form and symplectic connection -- are dynamical, and the resulting…
We show that the low-energy effective actions of two ten-dimensional supersymmetric heterotic strings are different by a $\mathbb{Z}_3$-valued discrete topological term even after we turn off the $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$…
A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator algebra and the corresponding…
In the present work the massless vector field in the de Sitter (dS) space has been quantized. "Massless" is used here by reference to conformal invariance and propagation on the dS light-cone whereas "massive" refers to those dS fields…
Given an automorphic line bundle ${\mathcal O}_X(k)$ of weight $k$ on the Drinfel'd upper half plane $X$ over a local field $K$, we construct a ${\rm GL}_2(K)$-equivariant integral lattice ${\mathcal O}_{\widehat{\mathfrak X}}(k)$ in…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous $(2+1)$-dimensional space-times with the sources given by the contributions of dilaton, antisymmetric…
An affine connection is said to be flat if its curvature tensor vanishes identically. Koszul-Vinberg (KV for abbreviation) cohomology has been invoked to study the deformation theory of flat and torsion-free affine connections on tangent…
Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be dramatically simplified by expressing them as double copies between field-theory amplitudes and scalar disk/sphere integrals, the latter…
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…
We study certain spinning strings exploring the flat directions of AdS3 x S3 x S3 x S1, the massless sector cousins of su(2) and sl(2) sector spinning strings. We describe these, and their vibrational modes, using the D(2,1;\alpha)^2…
We consider a two-point spatial lattice approximation to an open string moving in a flat background with B field. It gives a constrained dipole system under the influence of a vector potential. Solving and quantizing this system recover all…
Let $(E,\Phi)\rightarrow (X,\omega_X)$ be a Higgs bundle over a compact K\"ahler manifold. We suppose that the holomorphic vector bundle $E$ decomposes into a direct sum of holomorphic line bundles. In this paper, we give the necessary and…
We review a systematic construction of $\cx N=1$ supersymmetric heterotic string vacua using mirror symmetry. The method provides a large class of explicit solutions for stable, holomorphic vector bundles on Calabi-Yau n-folds Z_n in terms…
Free string theory on the plane-wave background displays a discrete Z2 symmetry exchanging the two transverse SO(4) rotation groups. This symmetry should be respected also at the interacting level. We show that the zero mode structure…
Double Field Theory suggests to view the whole massless sector of closed strings as the gravitational unity. The fundamental symmetries therein, including the $\mathbf{O}(D,D)$ covariance, can determine unambiguously how the Standard Model…