Abstract
We consider the inhomogeneous decay of an unstable D-brane of bosonic string theory in a linear dilaton background in a light-cone frame. At the lowest level, the dynamical equation that describes this process is a generalisation (that includes nonlocality and time delay) of a reaction-diffusion equation studied by Fisher (and others). We argue that the equation of motion of the cubic open string field theory is satisfied at least to the second order when we start with this `Fisher deformation', a marginal operator which has a simple pole term in its OPE. We also compute the one-point functions of closed string operators on the disc in the presence of this deformation.
Highlights
JHEP03(2014)015 other coordinate y along the brane) was found to have a close resemblance to the ubiquitous reaction-diffusion equation pioneered in refs. [12] and [13, 14]
We argue that the equation of motion of the cubic open string field theory is satisfied at least to the second order when we start with this ‘Fisher deformation’, a marginal operator which has a simple pole term in its OPE
There is a continuous family of marginal operators, we shall see that only one of these allows for a solution to the equations at second order
Summary
Let us, for definiteness, consider the CFT corresponding to an unstable Dp-brane of the bosonic string theory. Let us retain only the tachyon field φ (level truncation to zeroth order) and further restrict to spatially homogeneous decay, i.e., φ depends only on time t. This analysis was done in detail in ref. As a result of the non-local non-linear interactions, these behave wildly These authors did not find a solution that interpolates between the D-brane and the (closed string) vacuum. √ where K = 3 3/4, α = ln K and x⊥ denotes the coordinates along the D-brane that are transverse to the light-cone coordinates This has been referred to as the ‘Fisher equation for the tachyon on a decaying brane’ in [11]. I.e., O(1) in ε, the front is just as in figure 1—higher order corrections, can be found systematically following ref. [11]
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