Axial U(1) current in Grabowska and Kaplan's formulation

Recently, Grabowska and Kaplan suggested a non-perturbative formulation of a chiral gauge theory, which consists of the conventional domain-wall fermion and a gauge field that evolves by the gradient flow from one domain wall to the other. In this paper, we discuss the U(1) axial-vector current in 4 dimensions using this formulation. We introduce two sets of domain-wall fermions belonging to complex conjugate representations so that the effective theory is a 4-dimensional vector-like gauge theory. Then, as a natural definition of the axial-vector current, we consider a current that generates the simultaneous phase transformations for the massless modes in 4 dimensions. However, this current is exactly conserved and does not reproduce the correct anomaly. In order to investigate this point precisely, we consider the mechanism of the conservation. We find that this current includes not only the axial current on the domain wall but also a contribution from the bulk, which is non-local in the sense of 4-dimensional fields. Therefore, the local current is obtained by subtracting the bulk contribution from it.Comment: 25 pages, 1 figur

Reheating of the Universe as holographic thermalization

Assuming gauge/gravity correspondence we study reheating of the Universe using its holographic dual. Inflaton decay and thermalisation of the decay products correspond to collapse of a spherical shell and formation of a blackhole in the dual anti-de Sitter (AdS) spacetime. The reheating temperature is computed as the Hawking temperature of the developed blackhole probed by a dynamical boundary, and is determined by the inflaton energy density and the AdS radius, with corrections from the dynamics of the shell collapse. For given initial energy density of the inflaton field the holographic model gives significantly lower reheating temperature than the instant reheating scenario, while it is shown to be safely within phenomenological bounds.Comment: 5 pages, 1 figur

Improvement of energy-momentum tensor and non-Gaussianities in holographic cosmology

In holographic models of cosmology based on the (A)dS/CFT correspondence, conformal symmetry is implicit in the dual description of the Universe. Generically, however, one cannot expect the (broken) conformal invariance in the cosmic fluctuations as only the scale invariance is manifest in experiments. Also, in order for the prediction of the holographic models to make sense, the conformal symmetry needs to be broken as the scalar mode of the metric fluctuations becomes pure gauge in the conformal limit. We discuss the improvement ambiguity of the energy-momentum tensor in this context and construct a holographic model of the Universe that preserves the scale invariance but not necessarily the full conformal invariance. Our sample computation using a weakly coupled dual field theory shows that the orthogonal type of non-Gaussianity is present over and above the equilateral type. The improvement ambiguity corresponds to the choice of the energy momentum tensor that will couple to our particle physics sector after inflation. Our results show that the holographic prediction of the cosmological parameters crucially depends on such a choice

Hierarchical Cross-Modality Knowledge Transfer with Sinkhorn Attention for CTC-based ASR

Due to the modality discrepancy between textual and acoustic modeling, efficiently transferring linguistic knowledge from a pretrained language model (PLM) to acoustic encoding for automatic speech recognition (ASR) still remains a challenging task. In this study, we propose a cross-modality knowledge transfer (CMKT) learning framework in a temporal connectionist temporal classification (CTC) based ASR system where hierarchical acoustic alignments with the linguistic representation are applied. Additionally, we propose the use of Sinkhorn attention in cross-modality alignment process, where the transformer attention is a special case of this Sinkhorn attention process. The CMKT learning is supposed to compel the acoustic encoder to encode rich linguistic knowledge for ASR. On the AISHELL-1 dataset, with CTC greedy decoding for inference (without using any language model), we achieved state-of-the-art performance with 3.64% and 3.94% character error rates (CERs) for the development and test sets, which corresponding to relative improvements of 34.18% and 34.88% compared to the baseline CTC-ASR system, respectively.Comment: Submitted to ICASSP 202