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We discuss two physics-inspired approaches to derivation of the eigenfunctions and eigenvalues of $A_N$ Ruijsenaars-Schneider model. First approach which was recently proposed by the authors relies on the computations of superconformal indices of class $\mathcal{S}$ $4d$ ${\mathcal N}=2$ theories with the insertion of surface defects. Second approach uses computations of Nekrasov-Shatashvili limit of $5d$ ${\mathcal N} = 1^*$ instanton partition functions in the presence of co-dimension two defect. We compare results of these two approaches for the low-lying levels of Ruijsenaars-Schneider model. We also discuss different previously proposed exact quantization conditions for the Coulomb branch parameters of the instanton partition functions and their interpretations in terms of index calculations., Comment: 25 pages

We propose new constraints for 6d (1, 0) supergravity theories based on consistency conditions on the Kahler moduli spaces of their 5d reductions. The requirement that both the metric and the BPS string tensions in the Kahler moduli space are positive imposes specific restrictions on the Chern-Simons coefficients in the 5d effective Lagrangians that are derived from the Kaluza-Klein reductions of 6d theories. Moreover, the emergence of local interacting 5d CFTs when the moduli space metric degenerates introduces additional constraints coming from the analysis of 5d SCFTs. Focusing on the moduli spaces of 6d supergravity theories without a tensor multiplet and their Higgsings, we show that these constraints require the presence of certain primary states in the 2d worldvolume CFTs on 1/2 BPS strings. We specifically analyze a class of SU(2) models and infinite families of U(1) models using these constraints, and demonstrate that the theories featuring a 1-form symmetry in their massless spectra, unless the 1-form symmetry is gauged, fail to satisfy the constraints and therefore belong to the Swampland., Comment: 32 pages, v2: typos fixed, references added

A growth mindset has shown promising outcomes for increasing empathy ability. However, stimulating a growth mindset in VR-based empathy interventions is under-explored. In the present study, we implemented prosocial VR content, Our Neighbor Hero, focusing on embodying a virtual character to modulate players' mindsets. The virtual body served as a stepping stone, enabling players to identify with the character and cultivate a growth mindset as they followed mission instructions. We considered several implementation factors to assist players in positioning within the VR experience, including positive feedback, content difficulty, background lighting, and multimodal feedback. We conducted an experiment to investigate the intervention's effectiveness in increasing empathy. Our findings revealed that the VR content and mindset training encouraged participants to improve their growth mindsets and empathic motives. This VR content was developed for college students to enhance their empathy and teamwork skills. It has the potential to improve collaboration in organizational and community environments., Comment: 9 pages, 2 figures, 1 table

We present an efficient method to compute the modular extension of both fermionic topological orders and $\mathbb{Z}_2$-symmetric bosonic topological orders in two spatial dimensions, basing on congruence representations of $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups. To demonstrate the validity of our approach, we provide explicit calculations for topological orders with rank up to 10 for the fermionic cases and up to 6 for the bosonic cases. Along the way, we clarify the relation between fermionic rational conformal field theories, which live on the boundary of the corresponding fermionic topological orders, and modular extensions. In particular, we show that the $\mathrm{SL}_2(\mathbb{Z})$ representation of the R-R sector can be determined from the NS-NS sector using the modular extensions., Comment: 96 pages, no figure

We explore BPS strings in supergravity theories in six-dimensions and related Swampland Conjectures. We first propose a general modular ansatz for bootstrapping elliptic genera of 2d worldvolume theories on strings in the 6d theories. By employing mirror symmetry on F-theory examples, we explicitly compute the elliptic genera and validate our ansatz. We extend this approach to investigate BPS strings and their spectrum in non-geometric 6d theories which have no known F-theory constructions, and confirm the Swampland conjectures, including the Weak Gravity Conjecture, Distance Conjecture, and Emergent String Conjecture. We also discuss tensionless little strings that emerge near infinite-distance limits of strong gauge coupling in the moduli space of certain special theories., Comment: 72 pages, v2: minor corrections and references added

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O$7^+$-plane and O$7^-$-plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O$7^+$-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points., Comment: 10 pages, 6 figures

Glass surfaces of transparent objects and mirrors are not able to be uniquely and explicitly characterized by their visual appearances because they contain the visual appearance of other reflected or transmitted surfaces as well. Detecting glass regions from a single-color image is a challenging task. Recent deep-learning approaches have paid attention to the description of glass surface boundary where the transition of visual appearances between glass and non-glass surfaces are observed. In this work, we analytically investigate how glass surface boundary helps to characterize glass objects. Inspired by prior semantic segmentation approaches with challenging image types such as X-ray or CT scans, we propose separated internal-external boundary attention modules that individually learn and selectively integrate visual characteristics of the inside and outside region of glass surface from a single color image. Our proposed method is evaluated on six public benchmarks comparing with state-of-the-art methods showing promising results.

In this paper, using the De Giorgi-Nash-Moser method, we obtain an interior H\"older continuity of weak solutions to nonlocal $p$-Laplacian type Schr\"odinger equations given by an integro-differential operator ${\rm L}^p_K$ ($p>1$) as follows; $$\begin{cases} {\rm L}^p_K u+V|u|^{p-2} u=0 &\text{ in $\Omega$, } u=g &\text{ in ${\Bbb R}^n\setminus\Omega$ } \end{cases}$$ where $V=V_+-V_-$ with $(V_-,V_+)\in L^1_{loc}({\Bbb R}^n)\times L^q_{loc}({\Bbb R}^n)$ for $q>\frac{n}{ps}>1$ and $0\frac{n}{ps}>1, 0