LLM Magnons

We consider excitations of LLM geometries described by coloring the LLM plane with concentric black rings. Certain closed string excitations are localized at the edges of these rings. The string theory predictions for the energies of magnon excitations of these strings depends on the radii of the edges of the rings. In this article we construct the operators dual to these closed string excitations and show how to reproduce the string theory predictions for magnon energies by computing one loop anomalous dimensions. These operators are linear combinations of restricted Schur polynomials. The distinction between what is the background and what is the excitation is accomplished in the choice of the subgroup and the representations used to construct the operator.Comment: 42 pages, 4 figure

Topology Changing Transitions in Bubbling Geometries

Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.Comment: 24 pages, 8 figure

Exact operator bosonization of finite number of fermions in one space dimension

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the Hilbert space. In the bosonized theory the finiteness of the number of fermions appears as an ultraviolet cut-off. We discuss implications of this for the bosonized theory. We also discuss applications of our bosonization to one-dimensional fermion systems dual to (sectors of) string theory such as LLM geometries and c=1 matrix model.Comment: 47 pages, 1 figure; (v2) typos correcte

Rule-restricted Automaton-grammar transducers: Power and Linguistic Applications

This paper introduces the notion of a new transducer as a two-component system, which consists of a nite automaton and a context-free grammar. In essence, while the automaton reads its input string, the grammar produces its output string, and their cooperation is controlled by a set, which restricts the usage of their rules. From a theoretical viewpoint, the present paper discusses the power of this system working in an ordinary way as well as in a leftmost way. In addition, the paper introduces an appearance checking, which allows us to check whether some symbols are present in the rewritten string, and studies its e ect on the power. It achieves the following three main results. First, the system generates and accepts languages de ned by matrix grammars and partially blind multi-counter automata, respectively. Second, if we place a leftmost restriction on derivation in the context-free grammar, both accepting and generating power of the system is equal to generative power of context-free grammars. Third, the system with appearance checking can accept and generate all recursively enumerable languages. From more pragmatical viewpoint, this paper describes several linguistic applications. A special attention is paid to the Japanese-Czech translation

Incorporating Structured Commonsense Knowledge in Story Completion

The ability to select an appropriate story ending is the first step towards perfect narrative comprehension. Story ending prediction requires not only the explicit clues within the context, but also the implicit knowledge (such as commonsense) to construct a reasonable and consistent story. However, most previous approaches do not explicitly use background commonsense knowledge. We present a neural story ending selection model that integrates three types of information: narrative sequence, sentiment evolution and commonsense knowledge. Experiments show that our model outperforms state-of-the-art approaches on a public dataset, ROCStory Cloze Task , and the performance gain from adding the additional commonsense knowledge is significant

Exciting LLM Geometries

We study excitations of LLM geometries. These geometries arise from the backreaction of a condensate of giant gravitons. Excitations of the condensed branes are open strings, which give rise to an emergent Yang-Mills theory at low energy. We study the dynamics of the planar limit of these emergent gauge theories, accumulating evidence that they are planar ${\cal N}=4$ super Yang-Mills. There are three observations supporting this conclusion: (i) we argue for an isomorphism between the planar Hilbert space of the original ${\cal N}=4$ super Yang-Mills and the planar Hilbert space of the emergent gauge theory, (ii) we argue that the OPE coefficients of the planar limit of the emergent gauge theory vanish and (iii) we argue that the planar spectrum of anomalous dimensions of the emergent gauge theory is that of planar ${\cal N}=4$ super Yang-Mills. Despite the fact that the planar limit of the emergent gauge theory is planar ${\cal N}=4$ super Yang-Mills, we explain why the emergent gauge theory is not ${\cal N}=4$ super Yang-Mills theory.Comment: 30 pages plus Appendice