In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein four-manifolds such as AdS 4 , N = 1 rigidly supersymmetric sigma models are constrained to have target spaces with exact Kähler forms. Similarly, in gauged sigma models and gauge theories, we find that supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have the effect of enforcing that Kähler forms on quotient spaces be exact. We discuss the 'background principle' in this context. We also discuss general aspects of universality classes of gauged sigma models, as encoded by stacks, and also discuss affine bundle structures implicit in these constructions. In an appendix, we discuss how anomalies in four-dimensional gauge theories, such as those which play an important role in our analysis, can be recast in the language of stacks.

We study two-dimensional N =(0, 2) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider N =(0, 2) theories with an R-symmetry, which can always be defined on curved space by a pseudotopological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of N =(2, 2) GLSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the N =(2, 2) locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the N =(2, 2) locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold. Keywords: Supersymmetry, Topological Field Theory. A. Conventions and review of N =(0, 2) supersymmetry 40 A.1 Curved space conventions 40 A.2 N =(0, 2) supersymmetry in flat space 40 B. Elementary properties of the Grothendieck residue 43 C. One-loop determinants 44 C.1 Matter determinant for A/2-twisted GLSM with (2, 2) locus 44 C.2 Matter determinant for the B/2-twisted model 46 D.Čech-cohomology-based results for the correlation functions 46 D.1 P 1 × P 1 46 D.2Čech-cohomology-based results for F 1 49 R[E I ] = r I + 1 , R[J I ] = 1 − r I , (2.49) and such that Tr( Λ I E I ) and Tr(Λ I J I ) are gauge invariant.Anomaly cancelation imposes further constraints on the matter content and on the R-charge assignment. Let us decompose the gauge algebra g into semi-simple factors g α

In this paper we explore basic aspects of nonabelian (0,2) GLSMs in two dimensions for unitary gauge groups, an arena that until recently has largely been unexplored. We begin by discussing general aspects of (0,2) theories, including checks of dynamical supersymmetry breaking, spectators and weak coupling limits, and also build some toy models of (0,2) theories for bundles on Grassmannians, which gives us an opportunity to relate physical anomalies and trace conditions to mathematical properties. We apply these ideas to study (0,2) theories on Pfaffians, applying recent perturbative constructions of Pfaffians of Jockers et al. . We discuss how existing dualities in (2,2) nonabelian gauge theories have a simple mathematical understanding, and make predictions for additional dualities in (2,2) and (0,2) gauge theories. Finally, we outline how duality works in open strings in unitary gauge theories, and also describe why, in general terms, we expect analogous dualities in (0,2) theories to be comparatively rare.

Abstract. Jinping Underground lab for Nuclear Astrophysics (JUNA) will take the advantage of the ultralow background in Jinping underground lab, high current accelerator based on an ECR source and highly sensitive detector to study directly a number of crucial reactions to the hydrostatic stellar evolution for the first time at their relevant stellar energies. In its first phase, JUNA aims at the direct measurements of 25 Mg(p,γ) 26 Al, 19 F(p,α) 16 O, 13 C(α,n) 16 O and 12 C(α,γ) 16 O. The experimental setup, which include the accelerator system with high stability and high intensity, the detector system, and the shielding material with low background, will be established during the above research. The current progress of JUNA will be given. Article available at

Abstract. Jinping Underground lab for Nuclear Astrophysics (JUNA) will take the advantage of the ultralow background in Jinping underground lab, high current accelerator based on an ECR source and highly sensitive detector to study directly a number of crucial reactions to the hydrostatic stellar evolution for the first time at their relevant stellar energies. In its first phase, JUNA aims at the direct measurements of 25 Mg(p,γ) 26 Al, 19 F(p,α) 16 O, 13 C(α,n) 16 O and 12 C(α,γ) 16 O. The experimental setup, which include the accelerator system with high stability and high intensity, the detector system, and the shielding material with low background, will be established during the above research. The current progress of JUNA will be given. Article available at