Correlation Functions of Warped CFT

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green's function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS.Comment: 20 pages, 0 figur

Gravitational waves in gauge theory gravity with a negative cosmological constant

In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacements and rotations. Similar to the electromagnetism, the gauge formulation enable us to interpret the gravitational force as a gauge force on the background flat spacetime. The dynamical fields that describe the gravitational interactions are those position and rotation gauge fields introduced as the requirement of the gauge covariance. The gravitational field equations can be derived from the least action principle with the action as a gauge invariant quantity built from the covariant field strength. We discuss the gravitational wave solutions of the field equations with a negative cosmological constant, and show that the solution is of Petrov type-N. We also discuss the velocity memory effect in the gauge theory gravity by calculating the velocity change of an initially free falling massive particle after the passing a gravitational impulsive wave.Comment: 31 pages, 3 figure

Auto-Encoding Scene Graphs for Image Captioning

We propose Scene Graph Auto-Encoder (SGAE) that incorporates the language inductive bias into the encoder-decoder image captioning framework for more human-like captions. Intuitively, we humans use the inductive bias to compose collocations and contextual inference in discourse. For example, when we see the relation `person on bike', it is natural to replace `on' with `ride' and infer `person riding bike on a road' even the `road' is not evident. Therefore, exploiting such bias as a language prior is expected to help the conventional encoder-decoder models less likely overfit to the dataset bias and focus on reasoning. Specifically, we use the scene graph --- a directed graph ($\mathcal{G}$) where an object node is connected by adjective nodes and relationship nodes --- to represent the complex structural layout of both image ($\mathcal{I}$) and sentence ($\mathcal{S}$). In the textual domain, we use SGAE to learn a dictionary ($\mathcal{D}$) that helps to reconstruct sentences in the $\mathcal{S}\rightarrow \mathcal{G} \rightarrow \mathcal{D} \rightarrow \mathcal{S}$ pipeline, where $\mathcal{D}$ encodes the desired language prior; in the vision-language domain, we use the shared $\mathcal{D}$ to guide the encoder-decoder in the $\mathcal{I}\rightarrow \mathcal{G}\rightarrow \mathcal{D} \rightarrow \mathcal{S}$ pipeline. Thanks to the scene graph representation and shared dictionary, the inductive bias is transferred across domains in principle. We validate the effectiveness of SGAE on the challenging MS-COCO image captioning benchmark, e.g., our SGAE-based single-model achieves a new state-of-the-art $127.8$ CIDEr-D on the Karpathy split, and a competitive $125.5$ CIDEr-D (c40) on the official server even compared to other ensemble models