On instantons as Kaluza-Klein modes of M5-branes

Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of (noncommutative) U(1) instantons for any instanton number, and also show that charged instantons in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.1156sciescopu

Topological Chern-Simons Sigma Model

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to offer a new perspective on Casson invariant and its relation to Rozansky-Witten theory.Comment: 31 pages, no figure; v2. references adde

Janus and Multifaced Supersymmetric Theories

We investigate the various properties Janus supersymmetric Yang-Mills theories. A novel vacuum structure is found and BPS monopoles and dyons are studied. Less supersymmetric Janus theories found before are derived by a simpler method. In addition, we find the supersymmetric theories when the coupling constant depends on two and three spatial coordinates.Comment: 20 pages, no figures, typos, equations corrected. Additional comment

On instantons as Kaluza-Klein modes of M5-branes

Instantons and W-bosons in 5d maximally supersymmetric Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of (noncommutative) U(1) instantons for any instanton number, and also show that charged instantons in the Coulomb phase correctly give the degeneracy of SU(2) self-dual strings. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally show that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.Comment: 54 pages, 2 figures. v2: references added, figure improved, added comments on self-dual string anomaly, added new materials on the symmetric phase index, other minor correction

Superconformal Index with Duality Domain Wall

We study a superconformal index for ${\cal N}=4$ super Yang-Mills on $S^1 \times S^3$ with a half BPS duality domain wall inserted at the great two-sphere in $S^3$. The index is obtained by coupling the 3d generalized superconformal index on the duality domain wall with 4d half-indices. We further consider insertions of line operators to the configuration and propose integral equations which express that the 3d index on duality domain wall is a duality kernel relating half indices of two line operators related by the duality map. We explicitly check the proposed integral equations for various duality domain walls and line operators in the ${\cal N}=4$ SU(2) theory. We also briefly comment on a generalization to $\mathcal{N}=2$ $A_1$ Gaiotto theories with a simple example, ${\cal N}=2$ SU(2) SYM with four flavors.Comment: v1: 25 pages, 4 figures. v2: comments and a reference added, minor corrections. v3: 30 pages, new results and discussions added to sec 4.5 and sec 5.1, eq 49 and eq 51 corrected, text improved; to appear in JHE

Opposing Regulation of PROX1 by Interleukin-3 Receptor and NOTCH Directs Differential Host Cell Fate Reprogramming by Kaposi Sarcoma Herpes Virus

Lymphatic endothelial cells (LECs) are differentiated from blood vascular endothelial cells (BECs) during embryogenesis and this physiological cell fate specification is controlled by PROX1, the master regulator for lymphatic development. When Kaposi sarcoma herpes virus (KSHV) infects host cells, it activates the otherwise silenced embryonic endothelial differentiation program and reprograms their cell fates. Interestingly, previous studies demonstrated that KSHV drives BECs to acquire a partial lymphatic phenotype by upregulating PROX1 (forward reprogramming), but stimulates LECs to regain some BEC-signature genes by downregulating PROX1 (reverse reprogramming). Despite the significance of this KSHV-induced bidirectional cell fate reprogramming in KS pathogenesis, its underlying molecular mechanism remains undefined. Here, we report that IL3 receptor alpha (IL3Rα) and NOTCH play integral roles in the host cell type-specific regulation of PROX1 by KSHV. In BECs, KSHV upregulates IL3Rα and phosphorylates STAT5, which binds and activates the PROX1 promoter. In LECs, however, PROX1 was rather downregulated by KSHV-induced NOTCH signal via HEY1, which binds and represses the PROX1 promoter. Moreover, PROX1 was found to be required to maintain HEY1 expression in LECs, establishing a reciprocal regulation between PROX1 and HEY1. Upon co-activation of IL3Rα and NOTCH, PROX1 was upregulated in BECs, but downregulated in LECs. Together, our study provides the molecular mechanism underlying the cell type-specific endothelial fate reprogramming by KSHV