M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models

We study the 6d N=(0,2) superconformal field theory, which describes multiple M5-branes, on the product space S^2 x M_4, and suggest a correspondence between a 2d N=(0,2) half-twisted gauge theory on S^2 and a topological sigma-model on the four-manifold M_4. To set up this correspondence, we determine in this paper the dimensional reduction of the 6d N=(0,2) theory on a two-sphere and derive that the four-dimensional theory is a sigma-model into the moduli space of solutions to Nahm's equations, or equivalently the moduli space of k-centered SU(2) monopoles, where k is the number of M5-branes. We proceed in three steps: we reduce the 6d abelian theory to a 5d Super-Yang-Mills theory on I x M_4, with I an interval, then non-abelianize the 5d theory and finally reduce this to 4d. In the special case, when M_4 is a Hyper-Kahler manifold, we show that the dimensional reduction gives rise to a topological sigma-model based on tri-holomorphic maps. Deriving the theory on a general M_4 requires knowledge of the metric of the target space. For k=2 the target space is the Atiyah-Hitchin manifold and we twist the theory to obtain a topological sigma-model, which has both scalar fields and self-dual two-forms.Comment: 78 pages, 2 figure

Discovering Black Hole Mass Scaling Relations with Symbolic Regression

Our knowledge of supermassive black holes (SMBHs) and their relation to their host galaxies is still limited, and there are only around 150 SMBHs that have their masses directly measured and confirmed. Better black hole mass scaling relations will help us reveal the physics of black holes, as well as predict black hole masses that are not yet measured. Here, we apply symbolic regression, combined with random forest to those directly-measured black hole masses and host galaxy properties, and find a collection of higher-dimensional (N-D) black hole mass scaling relations. These N-D black hole mass scaling relations have scatter smaller than any of the existing black hole mass scaling relations. One of the best among them involves the parameters of central stellar velocity dispersion, bulge-to-total ratio, and density at the black hole's sphere-of-influence with an intrinsic scatter of $\epsilon=0.083\,\ \text{dex}$, significantly lower than$\epsilon \sim 0.3\,\ \text{dex}$for the M-$\sigma$ relation. These relations will inspire black hole physics, test black hole models implemented in simulations, and estimate unknown black hole masses on an unprecedented precision.Comment: 9 pages, 3 figures, accepted by NeurIPS 2023 workshop on Machine Learning and the Physical Science

Discovery of a Planar Black Hole Mass Scaling Relation for Spiral Galaxies

Supermassive black holes (SMBHs) are tiny in comparison to the galaxies they inhabit, yet they manage to influence and coevolve along with their hosts. Evidence of this mutual development is observed in the structure and dynamics of galaxies and their correlations with black hole mass ($M_\mathrm{BH}$). For our study, we focus on relative parameters that are unique to only disk galaxies. As such, we quantify the structure of spiral galaxies via their logarithmic spiral-arm pitch angles ($\phi$) and their dynamics through the maximum rotational velocities of their galactic disks ($v_\mathrm{max}$). In the past, we have studied black hole mass scaling relations between $M_\mathrm{BH}$ and $\phi$ or $v_\mathrm{max}$, separately. Now, we combine the three parameters into a trivariate $M_\mathrm{BH}$-$\phi$-$v_\mathrm{max}$ relationship that yields best-in-class accuracy in prediction of black hole masses in spiral galaxies. Because most black hole mass scaling relations have been created from samples of the largest SMBHs within the most massive galaxies, they lack certainty when extrapolated to low-mass spiral galaxies. Thus, it is difficult to confidently use existing scaling relations when trying to identify galaxies that might harbor the elusive class of intermediate-mass black holes (IMBHs). Therefore, we offer our novel relationship as an ideal predictor to search for IMBHs and probe the low-mass end of the black hole mass function by utilizing spiral galaxies. Already with rotational velocities widely available for a large population of galaxies and pitch angles readily measurable from uncalibrated images, we expect that the $M_\mathrm{BH}$-$\phi$-$v_\mathrm{max}$ fundamental plane will be a useful tool for estimating black hole masses, even at high redshifts.Comment: Unedited manuscript (12 pages & 4 figures), accepted for publication by The Astrophysical Journal Letters on September 15, 202

Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions

We have performed numerical simulations of SU(3) gauge theory coupled to Nf=2 flavors of symmetric representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length L=6, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.Comment: 12 pages, 11 figure

Predicting Second and Third Graders' Reading Comprehension Gains: Observing Students' and Classmates Talk during Literacy Instruction using COLT.

This paper introduces a new observation system that is designed to investigate students' and teachers' talk during literacy instruction, Creating Opportunities to Learn from Text (COLT). Using video-recorded observations of 2nd-3rd grade literacy instruction (N=51 classrooms, 337 students, 151 observations), we found that nine types of student talk ranged from using non-verbal gestures to generating new ideas. The more a student talked, the greater were his/her reading comprehension (RC) gains. Classmate talk also predicted RC outcomes (total effect size=0.27). We found that 11 types of teacher talk ranged from asking simple questions to encouraging students' thinking and reasoning. Teacher talk predicted student talk but did not predict students' RC gains directly. Findings highlight the importance of each student's discourse during literacy instruction, how classmates' talk contributes to the learning environments that each student experiences, and how this affects RC gains, with implications for improving the effectiveness of literacy instruction

Translanguaging for Higher Education Learning: Perspectives From International Students in Thailand

International student mobility is a common phenomenon observed globally, especially in higher education settings where English is used as the main medium of instruction. In such settings, international students may find themselves using English along with their first language for social or academic purposes. This study examines international students’ perspectives towards translanguaging in a university setting. With a mixed-methods approach, an anonymous online questionnaire and open-ended survey were distributed to international students. A total of 74 international students comprising 16 nationalities completed the survey. From the quantitative data, the students indicated a generally positive perspective towards translanguaging, especially to become more confident in English use and to relate better with other international students. Further quantitative analysis indicated that the perceptions differed significantly across years of study. The qualitative data provided further insights regarding translanguaging, namely the suitability of using a shared language in a formal learning context, such as in the classroom. All in all, this study was able to provide further insights into international students’ perspectives towards translanguaging

The Singular Hydrodynamic Interactions Between Two Spheres In Stokes Flow

We study exact solutions for the slow viscous flow of an infinite liquid caused by two rigid spheres approaching each either along or parallel to their line of centres, valid at all separations. This goes beyond the applicable range of existing solutions for singular hydrodynamic interactions (HIs) which, for practical applications, are limited to the near-contact or far field region of the flow. For the normal component of the HI, by use of a bipolar coordinate system, we derive the stream function for the flow as $Re\to 0$ and a formula for the singular (squeeze) force between the spheres as an infinite series. We also obtain the asymptotic behaviour of the forces as the nondimensional separation between the spheres goes to zero and infinity, rigorously confirming and improving upon known results relevant to a widely accepted lubrication theory. Additionally, we recover the force on a sphere moving perpendicularly to a plane as a special case. For the tangential component, again by using a bipolar coordinate system, we obtain the corresponding infinite series expression of the (shear) singular force between the spheres. All results hold for retreating spheres, consistent with the reversibility of Stokes flow. We demonstrate substantial differences in numerical simulations of colloidal fluids when using the present theory compared with existing multipole methods. Furthermore, we show that the present theory preserves positive definiteness of the resistance matrix $\boldsymbol{R}$ in a number of situations in which positivity is destroyed for multipole/perturbative methods.Comment: 28 pages, 12 Figure