Large-small dualities between periodic collapsing/expanding branes and brane funnels

Abstract

We consider space and time dependent fuzzy spheres $S^{2p}$ arising in $D1-D(2p+1)$ intersections in IIB string theory and collapsing D(2p)-branes in IIA string theory. In the case of $S^2$, where the periodic space and time-dependent solutions can be described by Jacobi elliptic functions, there is a duality of the form $r$ to $\frac{1}{r}$ which relates the space and time dependent solutions. This duality is related to complex multiplication properties of the Jacobi elliptic functions. For $S^4$ funnels, the description of the periodic space and time dependent solutions involves the Jacobi Inversion problem on a hyper-elliptic Riemann surface of genus 3. Special symmetries of the Riemann surface allow the reduction of the problem to one involving a product of genus one surfaces. The symmetries also allow a generalisation of the $r$ to $\frac{1}{r}$ duality. Some of these considerations extend to the case of the fuzzy $S^6$.

Latex, 50 pages, 2 figures ; v2 : a systematic typographical error corrected + minor changes

References in corpus (19)

• Born-Infeld particles and Dirichlet p-branes
• Tachyon Dynamics in Open String Theory
• Brane Dynamics From the Born-Infeld Action
• The Noncommutative Bion Core
• On spherical harmonics for fuzzy spheres in diverse dimensions
• Non-abelian Brane Intersections
• Longitudinal 5-branes as 4-spheres in Matrix theory
• BPS States of the Non-Abelian Born-Infeld Action
• BPS Monopoles
• Les Houches Lectures on Strings and Arithmetic
• Born-Infeld String as a Boundary Conformal Field Theory
• A Geometric Interpretation of the Open String Tachyon
• Spacelike and Time Dependent Branes from DBI
• Resolving brane collapse with 1/N corrections in non-Abelian DBI
• Non-Abelian BIonic Brane Intersections
• Solutions of Einstein's field equations related to Jacobi's inversion problem
• Lax representation for two--particle dynamics splitting on two tori
• Generating a dynamical M2 brane from super-gravitons in a pp-wave background
• Dynamical brane creation and annihilation via a background flux

Cited by in corpus (9)

• Finite N effects on the collapse of fuzzy spheres
• Fuzzy Sphere Dynamics and Non-Abelian DBI in Curved Backgrounds
• M2-branes stretching between M5-branes
• Noncommutative geometry, Quantum effects and DBI-scaling in the collapse of D0-D2 bound states
• Fluctuating Fuzzy Funnels
• Electrified Fuzzy Spheres and Funnels in Curved Backgrounds
• On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres
• Dynamics of Antimembranes in the Maximally Supersymmetric Eleven-Dimensional pp Wave
• Brane Intersections in the Presence of a Worldvolume Electric Field