Line defects and 5d instanton partition functions

We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter $x$, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N. Nekrasov is briefly discussed.Comment: 17 pages, 1 figure; typos fixed, references corrected; version to be published in JHE

?????? ????????? ???????????? ????????? ????????? ?????????????????? ??????????????? ?????????????????? ??????

Department of Chemical EngineeringUtilizing carbon dioxide to valuable chemicals is attractive technology for reducing CO2 emission. Among the chemicals converted from CO2, formic acid is one of the most valuable chemicals. Efficient conversion of CO2 to formic acid by electro-biocatalytic system was reported without expensive cofactor and noble metals. In this study, Shewanella oneidensis MR-1 (S. oneidensis MR-1) and encapsulated Formate dehydrogenase1 from Methylobacterium extorquens AM1 (MeFDH1) were applied to electro-biocatalytic reaction as a whole cell and encapsulated biocatalyst, respectively. First, S. oneidensis MR-1, when aerobically grown in Luria-Bertani (LB) medium, exhibited its ability for the conversion of CO2 into formic acid with productivity of 0.59 mM???hr-1 for 24 hr. In addition, CO2 reduction reaction catalyzed by S. oneidensis MR-1, when anaerobically grown in newly optimized LB medium supplemented with fumarate and nitrate, exhibited 3.2-fold higher productivity (1.9 mM???hr-1 for 72 hr). Second, previous study has demonstrated that electro-biocatalytic conversion of CO2 to formic acid by engineered MeFDH1 shows higher productivity than wild type. To increase physical strength, stability, reusability of MeFDH1, MeFDH1 was encapsulated in pure alginate and alginate silica hybrid beads. Michaelis-Menten kinetic constants demonstrated that binding affinity and maximum reaction rate of both encapsulated MeFDH1 were declined. Compared with pure alginate beads (5.4%), alginate-silica hybrid beads (67.4%) exhibited more higher recycling productivity after 4 cycles. These results show that the immobilization of MeFDH1 through encapsulation of by alginate-silica hybrid is a more suitable method to recycle formate production and prevent leakage of MeFDH1.ope

Self-heating of Strongly Interacting Massive Particles

It was recently pointed out that semi-annihilating dark matter (DM) may experience a novel temperature evolution dubbed as self-heating. Exothermic semi-annihilation converts the DM mass to the kinetic energy. This yields a unique DM temperature evolution, $T_{\chi} \propto 1 / a$, in contrast to $T_{\chi} \propto 1 / a^{2}$ for free-streaming non-relativistic particles. Self-heating continues as long as self-scattering sufficiently redistributes the energy of DM particles. In this paper, we study the evolution of cosmological perturbations in self-heating DM. We find that sub-GeV self-heating DM leaves a cutoff on the subgalactic scale of the matter power spectrum when the self-scattering cross section is $\sigma_{\rm self} / m_{\chi} \sim {\cal O} (1) \,{\rm cm}^{2} /{\rm g}$. Then we present a particle physics realization of the self-heating DM scenario. The model is based on recently proposed strongly interacting massive particles with pion-like particles in a QCD-like sector. Pion-like particles semi-annihilate into an axion-like particle, which is thermalized with dark radiation. The dark radiation temperature is smaller than the standard model temperature, evading the constraint from the effective number of neutrino degrees of freedom. It is easily realized when the dark sector is populated from the standard model sector through a small coupling.Comment: 25 pages, 5 figures; minor corrections, version accepted in PR

Topological triviality of smoothly knotted surfaces in 4-manifolds

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we construct examples of knotted surfaces whose complements have cyclic fundamental groups.Comment: Final version; appeared in AMS Transactions. 15 pages, 2 figure