Neural Representations of Courtship Song in the Drosophila Brain

Acoustic communication in drosophilid flies is based on the production and perception of courtship songs, which facilitate mating. Despite decades of research on courtship songs and behavior in Drosophila, central auditory responses have remained uncharacterized. In this study, we report on intracellular recordings from central neurons that innervate the Drosophila antennal mechanosensory and motor center (AMMC), the first relay for auditory information in the fly brain. These neurons produce graded-potential (nonspiking) responses to sound; we compare recordings from AMMC neurons to extracellular recordings of the receptor neuron population [Johnston's organ neurons (JONs)]. We discover that, while steady-state response profiles for tonal and broadband stimuli are significantly transformed between the JON population in the antenna and AMMC neurons in the brain, transient responses to pulses present in natural stimuli (courtship song) are not. For pulse stimuli in particular, AMMC neurons simply low-pass filter the receptor population response, thus preserving low-frequency temporal features (such as the spacing of song pulses) for analysis by postsynaptic neurons. We also compare responses in two closely related Drosophila species, Drosophila melanogaster and Drosophila simulans, and find that pulse song responses are largely similar, despite differences in the spectral content of their songs. Our recordings inform how downstream circuits may read out behaviorally relevant information from central neurons in the AMMC

String Field Theory from IIB Matrix Model

We derive Schwinger-Dyson equations for the Wilson loops of a type IIB matrix model. Superstring coordinates are introduced through the construction of the loop space. We show that the continuum limit of the loop equation reproduces the light-cone superstring field theory of type IIB superstring in the large-N limit. We find that the interacting string theory can be obtained in the double scaling limit as it is expected.Comment: 21 pages, Latex, 1 figur

Heisenberg and Modular Invariance of N=2 Conformal Field Theory

We present a theta function representation of the twisted characters for the rational N=2 superconformal field theory, and discuss the Jacobi-form like functional properties of these characters for a fixed central charge under the action of a finite Heisenberg group and modular transformations.Comment: 21 pages, Latex, 1 figure; minor typos corrected--Journal versio

Poincar\'{e} gauge theory of gravity

A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most general gravitational Lagrangian density, which is at most quadratic in curvature and torsion tensors and invariant under local Lorentz transformations and under general coordinate transformations, is given. Gravitational field equations are studied in detail, and solutions of the equations for weak gravitational fields are examined for the case with a static, \lq \lq spin"less point like source. We find, among other things, the following: (1)Solutions of the vacuum Einstein equation satisfy gravitational field equations in the vacuum in this theory. (2)For a class of the parameters in the gravitational Lagrangian density, the torsion is \lq \lq frozen" at the place where \lq \lq spin" density of the source field is not vanishing. In this case, the field equation actually agrees with the Einstein equation, when the source field is \lq \lq spin"less. (3)A teleparallel theory developed in a previous paper is \lq \lq included as a solution" in a limiting case. (4)A Newtonian limit is obtainable, if the parameters in the Lagrangian density satisfy certain conditions.Comment: 27pages, RevTeX, OCU-PHYS-15

Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions

The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and the associated twisted Witten indices are investigated with due attention to their behaviors in orbifoldization. Our findings are illustrated by and applied to several concrete examples. We give a better understanding of the duality phenomenon observed long before for certain Landau-Ginzburg models. We revisit and prove an old conjecture of Witten which states that every ADE Landau-Ginzburg model and the corresponding minimal model share the same elliptic genus. Mathematically, we establish ADE generalizations of the quintuple product identity.Comment: 28 pages; v2 refs adde

An Approach to Higher Dimensional Theories Based on Lattice Gauge Theory

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram.Comment: Lattice2003(higgs

Two-Dimensional Quantum Gravity in Temporal Gauge

We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c\!=\!0$ string field theory which was discovered recently. In particular, the pregeometric form of the Hamiltonian is naturally reproduced.Comment: 24 pages, 1 uuencoded figure, LaTeX file, YITP/K-1045. (Added detailed explanation and references.