A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
5-dim Superconformal Index with Enhanced En Global Symmetry
6 Pith papers cite this work, alongside 237 external citations. Polarity classification is still indexing.
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abstract
The five-dimensional $\mathcal{N}=1$ supersymmetric gauge theory with Sp(N) gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes with $N_f$ D8-branes on top of a single O8 orientifold plane in Type I' theory. This theory is known to be superconformal at the strong coupling limit with the enhanced global symmetry $E_{N_f+1}$ for $N_f\le 7$. In this work we calculate the superconformal index on $S^1\times S^4$ for the Sp(1) gauge theory by the localization method and confirm such enhancement of the global symmetry at the superconformal limit for $N_f\le 5$ to a few leading orders in the chemical potential. Both perturbative and (anti)instanton contributions are present in this calculation. For $N_f=6,7$ cases some issues related the pole structure of the instanton calculation could not be resolved and here we could provide only some suggestive answer for the leading contributions to the index. For the Sp(N) case, similar issues related to the pole structure appear.
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Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
The distinction between spinor and conjugate spinor matter in 5D SO(2N) gauge theories manifests as different boundary conditions on the Seiberg-Witten curve at O5-plane positions (w=±1).
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
citing papers explorer
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Shell formulas for instantons and gauge origami
A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
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Quantized Coulomb branch of 4d $\mathcal{N}=2$ $Sp(N)$ gauge theory and spherical DAHA of $(C_N^{\vee}, C_N)$-type
Quantized Coulomb branch of 4d N=2 Sp(N) theory with given matter content matches spherical DAHA of (C_N^vee, C_N) type, proven for N=1 and conjectured for higher N with 't Hooft loop evidence.
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Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations
Blow-up equation prefactors encode cubic 1-form self-anomalies and mixed anomalies of 5d N=1 SCFTs, deciding 2-group vs mixed anomaly structure.
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Thermodynamic limit for SO(2N) gauge theories with spinors/conjugate spinors
The distinction between spinor and conjugate spinor matter in 5D SO(2N) gauge theories manifests as different boundary conditions on the Seiberg-Witten curve at O5-plane positions (w=±1).
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Towards OSV in AdS
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
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