Related papers: The geometry of drums
In this highly speculative note we conjecture that it may be possible to understand features of coincident D-branes, such as the appearance of enhanced non-abelian gauge symmetry, in a purely geometric fashion, using a form of geometry…
We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a…
We answer Mark Kac's famous question, "can one hear the shape of a drum?" in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all…
We investigate the open string modes, describing the world-volume of a D p-brane, for its cyclic symmetry in presence of a magnetic field. It is argued that the constant coordinate modes receive non-perturbative correction. We show that…
Electromagnetics and Acoustics on a bounded domain are governed by the Helmholtz's equation; when such a domain is a [pre-]fractal described by means of a `just-touching' Iterated Function System (IFS) spectral decomposition of the…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
This thesis is devoted to the construction and study of D-branes in some curved space-times in string theory. On the one hand, those D-branes are described geometrically as submanifolds subject to Born-Infeld effective dynamics. On the…
The goal of this paper is to re-examine D-brane Ramond-Ramond field couplings in the presence of a B-field. We will argue that the generalised geometry induced on the world volume by the B-field results in an important but subtle change on…
We use recently proposed translations isometries of pp-waves to construct D4 and D3 brane solutions, using T-duality transformations, in exactly solvable pp-wave background originating from $AdS_3\times S^3$ geometry. A unique property of…
A number of questions related to the length spectrum of surfaces are discussed and in particular the existence of pairs of surfaces which though not isometric are isospectral. Here by isospectral we mean that a pair of bodies have the same…
This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset G of the Grassmann bundle $G(p,TX)$ of tangent $p$-planes to a riemannian manifold $X$. This determines a nonlinear partial…
This work focuses on the length correction due to radiation effect of a duct discontinuity or at the surface of a perforated plate in the linear acoustic domain and at large wavelengths. Two results are obtained from the comparison of…
We prove existence of a measurable Riemannian structure on higher-dimensional harmonic Sierpinski gasket fractals and deduce Gaussian heat kernel bounds in the geodesic metric. Our proof differs from that given by Kigami for the usual…
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other…
We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using…
String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field.…
``Can one hear the shape of a drum?'' was a question posed (and made famous) by mathematician Mark Kac in the mid-1960s. It addresses whether a deeper connection exists between the resonance modes (eigenmodes) of a drum and its shape. Here…
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string…
In this paper, we study a new matrix theory based on non-BPS D-instantons in type IIA string theory and D-instanton - anti D-instanton system in type IIB string theory, which we call K-matrix theory. The theory correctly incorporates the…
We employ generalized complex geometry to investigate supersymmetric embeddings of D-brane probes in a large class of SU(2) structure manifolds. This class includes the gravity dual of mass deformation and marginal beta deformation of N=4…