88 research outputs found
Time-dependent backgrounds of 2D string theory: Non-perturbative effects
We study the non-perturbative corrections (NPC) to the partition function of
a compactified 2D string theory in a time-dependent background generated by a
tachyon source. The sine-Liouville deformation of the theory is a particular
case of such a background. We calculate the leading as well as the subleading
NPC using the dual description of the string theory as matrix quantum
mechanics. As in the minimal string theories, the NPC are classified by the
double points of a complex curve. We calculate them by two different methods:
by solving Toda equation and by evaluating the quasiclassical fermion wave
functions. We show that the result can be expressed in terms of correlation
functions of the bosonic field associated with the tachyon source and identify
the leading and the subleading corrections as the contributions from the
one-point (disk) and two-point (annulus) correlation functions.Comment: 37 pages, 2 figure
Exponentially-improved asymptotics of single and multidimensional integrals
Two different approaches for finding the exponentially improved asymptotic behaviour of integrals with saddlepoints are presented. Both rely on the deformation of the contours of integration and can be applied to single and multidimensional
integrals alike. The class of integrals studied is of the form
J J g(z1, ,zp)e-f{zu 'Zp,X)dz1 dz
Logarithmic catastrophes and Stokes's phenomenon in waves at horizons
Waves propagating near an event horizon display interesting features
including logarithmic phase singularities and caustics. We consider an acoustic
horizon in a flowing Bose-Einstein condensate where the elementary excitations
obey the Bogoliubov dispersion relation. In the hamiltonian ray theory the
solutions undergo a broken pitchfork bifurcation near the horizon and one might
therefore expect the associated wave structure to be given by a Pearcey
function, this being the universal wave function that dresses catastrophes with
two control parameters. However, the wave function is in fact an Airy-type
function supplemented by a logarithmic phase term, a novel type of wave
catastrophe. Similar wave functions arise in aeroacoustic flows from jet
engines and also gravitational horizons if dispersion which violates Lorentz
symmetry in the UV is included. The approach we take differs from previous
authors in that we analyze the behaviour of the integral representation of the
wave function using exponential coordinates. This allows for a different
treatment of the branches that gives rise to an analysis based purely on
saddlepoint expansions, which resolve the multiple real and complex waves that
interact at the horizon and its companion caustic. We find that the horizon is
a physical manifestation of a Stokes surface, marking the place where a wave is
born, and that the horizon and the caustic do not in general coincide: the
finite spatial region between them delineates a broadened horizon.Comment: 34 pages, 12 figure
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