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Register a new userc=1 String as a Topological Model
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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.
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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.
We clarify some aspects of the map between the c=1 string theory at self-dual radius and the topologically twisted cigar at level one. We map the ZZ and FZZT D-branes in the c=1 string theory at self dual radius to the localized and extended branes in the topological theory on the cigar. We show that the open string spectrum on the branes in the two theories are in correspondence with each other, and their two point correlators are equal. We also find a representation of an extended N=2 algebra on the worldsheet which incorporates higher spin currents in terms of asymptotic variables on the cigar.
A similarity transformation, which brings a particular class of the $N=1$ string to the $N=0$ one, is explicitly constructed. It enables us to give a simple proof for the argument recently proposed by Berkovits and Vafa. The $N=1$ BRST operator is turned into the direct sum of the corresponding $N=0$ BRST operator and that for an additional topological sector. As a result, the physical spectrum of these $N=1$ vacua is shown to be isomorphic to the tensor product of the $N=0$ spectrum and the topological sector which consists of only the vacuum. This transformation manifestly keeps the operator algebra.
We investigate how topological entanglement of Chern-Simons theory is captured in a string theoretic realization. Our explorations are motivated by a desire to understand how quantum entanglement of low energy open string degrees of freedom is encoded in string theory (beyond the oft discussed classical gravity limit). Concretely, we realize the Chern-Simons theory as the worldvolume dynamics of topological D-branes in the topological A-model string theory on a Calabi-Yau target. Via the open/closed topological string duality one can map this theory onto a pure closed topological A-model string on a different target space, one which is related to the original Calabi-Yau geometry by a geometric/conifold transition. We demonstrate how to uplift the replica construction of Chern-Simons theory directly onto the closed string and show that it provides a meaningful definition of reduced density matrices in topological string theory. Furthermore, we argue that the replica construction commutes with the geometric transition, thereby providing an explicit closed string dual for computing reduced states, and Renyi and von Neumann entropies thereof. While most of our analysis is carried out for Chern-Simons on S^3, the emergent picture is rather general. Specifically, we argue that quantum entanglement on the open string side is mapped onto quantum entanglement on the closed string side and briefly comment on the implications of our result for physical holographic theories where entanglement has been argued to be crucial ingredient for the emergence of classical geometry.
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