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In clinical practice, anisotropic volumetric medical images with low through-plane resolution are commonly used due to short acquisition time and lower storage cost. Nevertheless, the coarse resolution may lead to difficulties in medical diagnosis by either physicians or computer-aided diagnosis algorithms. Deep learning-based volumetric super-resolution (SR) methods are feasible ways to improve resolution, with convolutional neural networks (CNN) at their core. Despite recent progress, these methods are limited by inherent properties of convolution operators, which ignore content relevance and cannot effectively model long-range dependencies. In addition, most of the existing methods use pseudo-paired volumes for training and evaluation, where pseudo low-resolution (LR) volumes are generated by a simple degradation of their high-resolution (HR) counterparts. However, the domain gap between pseudo- and real-LR volumes leads to the poor performance of these methods in practice. In this paper, we build the first public real-paired dataset RPLHR-CT as a benchmark for volumetric SR, and provide baseline results by re-implementing four state-of-the-art CNN-based methods. Considering the inherent shortcoming of CNN, we also propose a transformer volumetric super-resolution network (TVSRN) based on attention mechanisms, dispensing with convolutions entirely. This is the first research to use a pure transformer for CT volumetric SR. The experimental results show that TVSRN significantly outperforms all baselines on both PSNR and SSIM. Moreover, the TVSRN method achieves a better trade-off between the image quality, the number of parameters, and the running time. Data and code are available at https://github.com/smilenaxx/RPLHR-CT.