Search

In the type IIB maximally supersymmetric pp-wave background, stringy excited modes are described by BMN (Berenstein-Madalcena-Nastase) operators in the dual $\mathcal{N}=4$ super-Yang-Mills theory. In this paper, we continue the studies of higher genus free BMN correlators with more stringy modes, mostly focusing on the case of genus one and four stringy modes in different transverse directions. Surprisingly, we find that the non negativity of torus two-point functions, which is a consequence of a previously proposed probability interpretation and has been verified in the cases with two and three stringy modes, is no longer true for the case of four or more stringy modes. Nevertheless, the factorization formula, which is also a proposed holographic dictionary relating the torus two-point function to a string diagram calculation, is still valid. We also check the correspondence of planar three-point functions with Green-Schwarz string vertex with many string modes. We discuss some issues in the case of multiple stringy modes in the same transverse direction. Our calculations provide some new perspectives on pp-wave holography., Comment: 39 pages, 3 figures. v2: journal version, references added

We make a proposal for calculating refined Gopakumar-Vafa numbers (GVN) on elliptically fibered Calabi-Yau 3-folds based on refined holomorphic anomaly equations. The key examples are smooth elliptic fibrations over (almost) Fano surfaces. We include a detailed review of existing mathematical methods towards defining and calculating the (unrefined) Gopakumar-Vafa invariants (GVI) and the GVNs on compact Calabi-Yau 3-folds using moduli of stable sheaves, in a language that should be accessible to physicists. In particular, we discuss the dependence of the GVNs on the complex structure moduli and on the choice of an orientation. We calculate the GVNs in many instances and compare the B-model predictions with the geometric calculations. We also derive the modular anomaly equations from the holomorphic anomaly equations by analyzing the quasi-modular properties of the propagators. We speculate about the physical relevance of the mathematical choices that can be made for the orientation., Comment: 92 pages, 2 pdf figures

We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev's quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period., Comment: 23 pages, no figure. v2: journal version

In real-world single image super-resolution (SISR) task, the low-resolution image suffers more complicated degradations, not only downsampled by unknown kernels. However, existing SISR methods are generally studied with the synthetic low-resolution generation such as bicubic interpolation (BI), which greatly limits their performance. Recently, some researchers investigate real-world SISR from the perspective of the camera and smartphone. However, except the acquisition equipment, the display device also involves more complicated degradations. In this paper, we focus on the camera-screen degradation and build a real-world dataset (Cam-ScreenSR), where HR images are original ground truths from the previous DIV2K dataset and corresponding LR images are camera-captured versions of HRs displayed on the screen. We conduct extensive experiments to demonstrate that involving more real degradations is positive to improve the generalization of SISR models. Moreover, we propose a joint two-stage model. Firstly, the downsampling degradation GAN(DD-GAN) is trained to model the degradation and produces more various of LR images, which is validated to be efficient for data augmentation. Then the dual residual channel attention network (DuRCAN) learns to recover the SR image. The weighted combination of L1 loss and proposed Laplacian loss are applied to sharpen the high-frequency edges. Extensive experimental results in both typical synthetic and complicated real-world degradations validate the proposed method outperforms than existing SOTA models with less parameters, faster speed and better visual results. Moreover, in real captured photographs, our model also delivers best visual quality with sharper edge, less artifacts, especially appropriate color enhancement, which has not been accomplished by previous methods.

We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on genus one mirror curves. We compute the spectra of the quantum systems both by standard perturbation method and by Bohr-Sommerfeld method with quantum periods as the phase volumes. In this way, we obtain some exact analytic results for the classical and quantum periods of the Calabi-Yau geometries. We also determine the differential operators of the quantum periods and compute the topological string free energy in Nekrasov-Shatashvili (NS) limit. The results agree with calculations from other methods such as the topological vertex., Comment: 40 pages, 3 figures. v2: minor corrections, published in JHEP

There is an interesting relation between the quantum periods on a certain limit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and a TBA (Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM (Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parameter generalization of the relation. Furthermore, we derive the differential operators for quantum periods and the TBA-like equation in various limits of the generalized relation., Comment: 13 pages, no figure. v2: journal version

In a previous paper, we proposed a probability interpretation for higher genus amplitudes of BMN (Berenstein-Maldacena-Nastase) strings in a pp-wave background with infinite negative curvature. This provides a natural definition of the entropy of a BMN string as the Shannon entropy of its corresponding probability distribution. We prove a universal upper bound that the entropy grows at most logarithmically in the strong string coupling limit. We also study the entropy by numerical methods and discuss some interesting salient features., Comment: 5 pages, 1 figure. v2: journal version, some revisions including a change of the title

In a previous paper we proposed a factorization principle for the correlation functions of Berenstein-Maldacena-Nastase (BMN) operators in free $\mathcal{N}=4$ super-Yang-Mills theory. These correlators are conjectured to described physical string amplitudes in an infinitely curved Ramond-Ramond pp-wave background. There was a puzzle that the factorization seems to break down for $S$-channel in the $2\rightarrow 2$ scattering process. Here we resolve this puzzle by including some diagrams missed in the previous paper. We also observe some interesting relations which further support the interpretation of higher genus correlators as physical string loop amplitudes., Comment: 22 pages, 9 figures. v2: major revisions in section 3. v3: minor clarifications, journal version. v4: a further correction about parameter counting in section 3

This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects of these developments. First, we discuss the computational progress in the topological string partition functions on a class of elliptic Calabi-Yau manifolds. We propose to use Jacobi forms as an ansatz for the partition function. For non-compact models, the techniques often provide complete solutions, while for compact models, though it is still not completely solvable, we compute to higher genus than previous works. Second, we explore a remarkable connection of refined topological strings on a class of non-compact toric Calabi-Yau threefolds with non-perturbative effects in quantum-mechanical systems. The connections provide rarely available exact quantization conditions for quantum systems and new insights on non-perturbative formulations of topological string theory., Comment: A review article of the author's recent research, 16 pages, 2 figures. Journal version for "Science China Physics, Mechanics & Astronomy"

Style transfer of polyphonic music recordings is a challenging task when considering the modeling of diverse, imaginative, and reasonable music pieces in the style different from their original one. To achieve this, learning stable multi-modal representations for both domain-variant (i.e., style) and domain-invariant (i.e., content) information of music in an unsupervised manner is critical. In this paper, we propose an unsupervised music style transfer method without the need for parallel data. Besides, to characterize the multi-modal distribution of music pieces, we employ the Multi-modal Unsupervised Image-to-Image Translation (MUNIT) framework in the proposed system. This allows one to generate diverse outputs from the learned latent distributions representing contents and styles. Moreover, to better capture the granularity of sound, such as the perceptual dimensions of timbre and the nuance in instrument-specific performance, cognitively plausible features including mel-frequency cepstral coefficients (MFCC), spectral difference, and spectral envelope, are combined with the widely-used mel-spectrogram into a timber-enhanced multi-channel input representation. The Relativistic average Generative Adversarial Networks (RaGAN) is also utilized to achieve fast convergence and high stability. We conduct experiments on bilateral style transfer tasks among three different genres, namely piano solo, guitar solo, and string quartet. Results demonstrate the advantages of the proposed method in music style transfer with improved sound quality and in allowing users to manipulate the output.