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Register a new userA modified c=1 matrix model with new critical behavior
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By introducing a $int dt , gleft(Tr Phi^2(t)right)^2$ term into the action of the $c=1$ matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical ``bubbles which touch one another at single points. At a special value of $g$, the sum over connected surfaces behaves as $Delta^2 logDelta$, where $Delta$ is the cosmological constant (the sum over surfaces of area $A$ goes as $A^{-3}$). For comparison, in the conventional $c=1$ model the sum over planar surfaces behaves as $Delta^2/ logDelta$.
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We study string interactions in the fermionic formulation of the c=1 matrix model. We give a precise nonperturbative description of the rolling tachyon state in the matrix model, and discuss S-matrix elements of the c=1 string. As a first step to study string interactions, we compute the interaction of two decaying D0-branes in terms of free fermions. This computation is compared with the string theory cylinder diagram using the rolling tachyon ZZ boundary states.
Classical particle motions in an inverse harmonic potential show the exponential sensitivity to initial conditions, where the Lyapunov exponent $lambda_L$ is uniquely fixed by the shape of the potential. Hence, if we naively apply the bound on the Lyapunov exponent $lambda_L le 2pi T/ hbar$ to this system, it predicts the existence of the bound on temperature (the lowest temperature) $T ge hbar lambda_L/ 2pi$ and the system cannot be taken to be zero temperature when $hbar eq 0$. This seems a puzzle because particle motions in an inverse harmonic potential should be realized without introducing any temperature but this inequality does not allow it. In this article, we study this problem in $N$ non-relativistic free fermions in an inverse harmonic potential ($c=1$ matrix model). We find that thermal radiation is {em induced} when we consider the system in a semi-classical regime even though the system is not thermal at the classical level. This is analogous to the thermal radiation of black holes, which are classically non-thermal but behave as thermal baths quantum mechanically. We also show that the temperature of the radiation in our model saturates the inequality, and thus, the system saturates the bound on the Lyapunov exponent, although the system is free and integrable. Besides, this radiation is related to acoustic Hawking radiation of the fermi fluid.
The discrete states in the $c=1$ string are shown to be the physical states of a certain topological sigma model. We define a set of new fields directly from $c=1$ variables, in terms of which the BRST charge and energy-momentum tensor are rewritten as those of the topological sigma model. Remarkably, ground ring generator $x$ turns out to be a coordinate of the sigma model. All of the discrete states realize a graded ring which contains ground ring as a subset.
We study fractional Skyrmions in a $mathbb{C}P^2$ baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on $mathbb{C}P^2$.
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