Splitting of surface defect partition functions and integrable systems

We study Bethe/gauge correspondence at the special locus of Coulomb moduli where the integrable system exhibits the splitting of degenerate levels. For this investigation, we consider the four-dimensional pure $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory, with a half-BPS surface defect constructed with the help of an orbifold or a degenerate gauge vertex. We show that the non-perturbative Dyson-Schwinger equations imply the Schr\"odinger-type and the Baxter-type differential equations satisfied by the respective surface defect partition functions. At the special locus of Coulomb moduli the surface defect partition function splits into parts. We recover the Bethe/gauge dictionary for each summand.Comment: 34 pages, 2 figures; v2. published versio

Additional file 1: of The genomic features of parasitism, Polyembryony and immune evasion in the endoparasitic wasp Macrocentrus cingulum

Figure S1. Flow cytometry estimation of the genome size for the M. cingulum. Figure S2. The distribution of 17-mer frequency in M. cingulum genome sequencing reads. Figure S3. Distribution of GC content, CpG Obs/ExpRatios of M. cingulum(Mcin), N. vitripennis(Nvit) and A. mellifera(Amel). Figure S4. COG function classification of the OGS in M. cingulum. Figure S5. KEGG pathway analysis of the OGS in M. cingulum. Figure S6. GO classification of the OGS in M. cingulum. Figure S7. Venn diagram of the homologous protein-coding genes among three wasps (M. cingulum, C. solmsi, N. vitripennis) and fruit fly (D. melanogaster). Figure S8. Phylogenetic relationship of CSP proteins from A. mellifera, C. floridanum, C. solmsi, M. cingulum, N.vitripennis, S.invicta. Figure S9. Phylogenetic relationship of GR proteins from A. mellifera, C. floridanum, C. solmsi, M. cingulum, N.vitripennis, S.invicta. Figure S10. Phylogenetic relationship of IR proteins from A. mellifera, C. floridanum, C. solmsi, M. cingulum, N.vitripennis, S.invicta. Figure S11. Phylogenetic relationship of OR proteins from C. floridanum, D. melanogaster and M. cingulum. Figure S12. Phylogenetic relationship of OBP proteins from A. mellifera, C. floridanum, C. solmsi, M. cingulum, N.vitripennis, S.invicta. Figure S13. Phylogenetic relationship of SNMP proteins from A.mellifera, C. floridanum, C. solmsi, M. cingulum, N.vitripennis, S.invicta. Figure S14. Phylogenetic relationship of GST proteins from A. mellifera, C. floridanum, C. solmsi, M. cingulum, N.vitripennis, S.invicta. Figure S15. Phylogenetic relationship of P450 proteins from N. vitripennis, D. melanogaster and M. cingulum. Figure S16. Phylogenetic relationship of ABC proteins from M. cingulum and D. melanogaster. Figure S17. Different expression levels of miR-14b in different developmental stages of M. cingulum.Table S1. Genome sequencing data of M. cingulum. Table S2. Estimation of M. cingulum genome size using K-mer analysis. Table S3. Summary of the M. cingulum genome assembly. Table S4. The published insect genomes. Table S5. The genome assembly assessment on different insects. Table S6. Classification of repeat sequences identified in the M. cingulum genome. Table S7. Genome features of the M. cingulum, N. vitripennis and A. mellifera. Table S8. Gene features of M. cingulum, N. vitripennis and A. mellifera. Table S9. The insects with OGSs in InsectBase. Table S10. Hemomucin genes in eight wasps. Table S11. The different gene expression of embryo and pseudogerm transcriptomes in KEGG pathway. Table S12. The differently expressed miRNAs in embryo and mixed embryo transcriptomes. Table S13. Comparison of gene numbers for chemoreception in A.mellifera, C. floridanum, C. solmsi, M. cingulum, N. vitripennis and S. invicta. Table S14. Comparison of gene numbers for Gene families associated with insecticide resistance and detoxification in D. melanogaster, A. mellifera, C. floridanum, C. solmsi, M. cingulum, N. vitripennis and S. invicta. Table S15. Comparison of gene numbers of insect immune in A. mellifera, C. floridanum, C. solmsi, M. cingulum, N. vitripennis and S. invicta. Table S16. The PCR primer for target genes of mci-miR-14b. (PDF 6076 kb