The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes

Based on work by Orlov, we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg theories correspond to matrix factorizations and the D-branes on the Calabi-Yau manifolds are objects in the derived category. We give several examples including branes on quotient singularities associated to weighted projective spaces. We are able to confirm several conjectures and statements in the literature.Comment: 24 pages, refs added + minor correctio

Infrasound initiates directional fast-start escape responses in juvenile roach Rutilus rutilus

Acoustic stimuli within the sonic range are effective triggers of C-type escape behaviours in fish. We have previously shown that fish have an acute sensitivity to infrasound also, with acceleration thresholds in the range of 10(-5) m s(-2). In addition, infrasound at high intensities around 10(-2) m s(-2) elicits strong and sustained avoidance responses in several fish species. In the present study, the possible triggering of C-escapes by infrasonic single-cycle vibrations was examined in juvenile roach Rutilus rutilus. The fish were accelerated in a controlled and quantifiable manner using a swing system. The applied stimuli simulated essential components of the accelerations that a small fish would encounter in the hydrodynamic flow field produced by a predatory fish. Typical C- and S-type escape responses were induced by accelerations within the infrasonic range with a threshold of 0.023 m s(-2) for an initial acceleration at 6.7 Hz. Response trajectories were on average in the same direction as the initial acceleration. Unexpectedly, startle behaviours mainly occurred in the trailing half of the test chamber, in which the fish were subjected to linear acceleration in combination with compression, i.e. the expected stimuli produced by an approaching predator. Very few responses were observed in the leading half of the test chamber, where the fish were subjected to acceleration and rarefaction, i.e. the stimuli expected from a suction type of predator. We conclude that particle acceleration is essential for the directionality of the startle response to infrasound, and that the response is triggered by the synergistic effects of acceleration and compression

Tachyon Condensation on the Elliptic Curve

We use the framework of matrix factorizations to study topological B-type D-branes on the cubic curve. Specifically, we elucidate how the brane RR charges are encoded in the matrix factors, by analyzing their structure in terms of sections of vector bundles in conjunction with equivariant R-symmetry. One particular advantage of matrix factorizations is that explicit moduli dependence is built in, thus giving us full control over the open-string moduli space. It allows one to study phenomena like discontinuous jumps of the cohomology over the moduli space, as well as formation of bound states at threshold. One interesting aspect is that certain gauge symmetries inherent to the matrix formulation lead to a non-trivial global structure of the moduli space. We also investigate topological tachyon condensation, which enables us to construct, in a systematic fashion, higher-dimensional matrix factorizations out of smaller ones; this amounts to obtaining branes with higher RR charges as composites of ones with minimal charges. As an application, we explicitly construct all rank-two matrix factorizations.Comment: 69p, 6 figs, harvmac; v2: minor change

Fractional two-branes, toric orbifolds and the quantum McKay correspondence

We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of orbifolds C^3/Z_n. We study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples -- the crepant resolutions of C^3/Z_3 and C^3/Z_5.Comment: 34 pages, 2 figures, LaTeX (JHEP3 style); (v2) typos corrected; (v3) sec 3 reorganise

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

Gauge theories from wrapped and fractional branes

We compare two applications of the gauge/gravity correspondence to a non conformal gauge theory, based respectively on the study of D-branes wrapped on supersymmetric cycles and of fractional D-branes on orbifolds. We study two brane systems whose geometry is dual to N=4, D=2+1 super Yang-Mills theory, the first one describing D4-branes wrapped on a two-sphere inside a Calabi-Yau two-fold and the second one corresponding to a system of fractional D2/D6-branes on the orbifold R^4/Z_2. By probing both geometries we recover the exact perturbative running coupling constant and metric on the moduli space of the gauge theory. We also find a general expression for the running coupling constant of the gauge theory in terms of the "stringy volume" of the two-cycle which is involved in both types of brane systems.Comment: AMS-LaTeX, 35 pages, no figures. Minor typos corrected, version to appear in NP

Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere

Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics, and leading to applications from energy harvesting to medical imaging. Here we use optically levitated nanospheres that are heated to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers new opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and a new means for testing non-equilibrium thermodynamicsComment: 5 pages, 4 figures, supplementary material available upon reques

Moduli Webs and Superpotentials for Five-Branes

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.Comment: 41 pages, 1 figur