Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons

By Nicolas Moeller, B. Zwiebach. 2002

277 citations recorded by the source corpus.

Both in string field theory and in p-adic string theory the equations of motion involve infinite number of time derivatives. We argue that the initial value problem is qualitatively different from that obtained in the limit of many time derivatives in that the space of initial conditions becomes strongly constrained. We calculate the energy-momentum tensor and study in detail time dependent solutions representing tachyons rolling on the p-adic string theory potentials. For even potentials we find surprising small oscillations at the tachyon vacuum. These are not conventional physical states but rather anharmonic oscillations with a nontrivial frequency-amplitude relation. When the potentials are not even, small oscillatory solutions around the bottom must grow in amplitude without a bound. Open string field theory resembles this latter case, the tachyon rolls to the bottom and ever growing oscillations ensue. We discuss the significance of these results for the issues of emerging closed strings and tachyon matter.

Subfields: Mathematical Physics, Pharmaceutical Science, Physiology

View Paper: https://www.semanticscholar.org/paper/ff544c6540da2b9bc64f7838ae2f57c8e637fba2

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Citations in the corpus

D-Branes, Tachyons, and String Field Theory (2003, result): “[6] In fact, the early attempts to describe the rolling of the tachyon in Witten’s string field theory [ 138 , 139] appear to be in contradiction with the results that follow from conformal field theory.”
Stable bounce and inflation in non-local higher derivative cosmology (2012, background): “This property also manifests in the way one is often able to replace the infinite differential equation of motion with an integral equation [11].”
Liouville Field Theory — A decade after the revolution (2004, unknown): “More detailed discussion on the D-brane decay can be found in [265], [266], [267], [211], [268], [212], [185], [269], [270], [271], [272], [273], [274], [275], [276], [277], [278], [279], [209], [280], [281], [282], [283], [284], [210], [285], [286], [287], [288].”
Modified Gravity and Cosmology (2011, background): “We will not discuss theories with infinite derivatives, as occur in string field theory, or p-adic string theory (see [904] for discussion of such theories).”
D-brane Decay in Two-Dimensional String Theory (2003, background): “A more detailed study of Dp-brane decay was carried out in [6-24] and led to many new insights.”
On p-adic mathematical physics (2006, methodology): “Nonlocal scalar field theory [18, 19] for p-adic strings has occurred to be very instructive toy model [44, 45] for truncated string field theory models [46].”
Nonlinear Equations with Infinitely many Derivatives (2011, background): “For example, it is stated in [17] that solutions to the p-adic string equation (3) should be analytic.”
Coupling of rolling tachyon to closed strings (2002, methodology): “In [1], he has presented an iterative scheme to construct a solution in Witten’s Open String Field Theory that describes the tachyon rolling up and down its potential in unstable D-brane systems (see also [4, 5, 6]).”
Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity (2010, unknown): “One alternative view would be to study fully non-perturbative and ghostfree higher derivative actions of gravity inspired from string theory [11]: An infinite set of higher derivative corrections (series expansion in α, the string tension) mostly in the form of an exponential are often known to appe”
Analytic solutions for marginal deformations in open string field theory (2007, result): “Is the correspondence between boundary CFT’s and classical OSFT solutions one-to-one?”
Closed strings from decaying D-branes (2003, background): “It was found that the late time evolution of the tachyon leads to a pressureless fluid, called “tachyon matter” (see however [15]).”