Solvable model of strings in a time dependent plane wave background
Nov, 2002
57 pages
Published in:
- Class.Quant.Grav. 20 (2003) 969-1016
e-Print:
- hep-th/0211289 [hep-th]
Report number:
- CERN-TH-2002-348,
- Imperial-TP-02-3-4
Citations per year
Abstract:
We investigate a string model defined by a special plane-wave metric ds^2 = 2dudv - l(u) x^2 du^2 + dx^2 with l(u) = k/u^2 and k=const > 0. This metric is a Penrose limit of some cosmological, Dp-brane and fundamental string backgrounds. Remarkably, in Rosen coordinates the metric has a ``null cosmology'' interpretation with flat spatial sections and scale factor which is a power of the light-cone time u. We show that: (i) This spacetime is a Lorentzian homogeneous space. In particular, like Minkowski space, it admits a boost isometry in u,v. (ii) It is an exact solution of string theory when supplemented by a u-dependent dilaton such that its exponent (i.e. effective string coupling) goes to zero at u=infinity and at the singularity u=0, reducing back-reaction effects. (iii) The classical string equations in this background become linear in the light-cone gauge and can be solved explicitly in terms of Bessel's functions: thus the string model can be directly quantized. This allows one to address the issue of singularity at the string-theory level. We examine the propagation of first-quantized point-particle and string modes in this time-dependent background. Using certain analytic continuation prescription we argue that string propagation through the singularity can be smooth.Note:
- 58 pages, latex. v2: several references to related previous work added
- string model
- space-time: singularity
- plane wave
- algebra: Lie
- algebra: Heisenberg
- Klein-Gordon equation: solution
- Schroedinger equation: solution
- Hamiltonian formalism
- group theory: geometrical
- vector: Killing
References(63)
Figures(4)