The topologically twisted index of $\mathcal{N}=4$ super-Yang-Mills on $T^2\times S^2$ and the elliptic genus

Abstract

We examine the topologically twisted index of $\mathcal{N}=4$ super-Yang-Mills with gauge group $SU(N)$ on $T^2\times S^2$, and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds $T^2/{\mathbb{Z}}_m\times {\mathbb{Z}}_n$ where $N=mn$. After summing over these sectors, the index can be expressed as the elliptic genus of a two-dimensional $\mathcal{N}=(0,2)$ theory resulting from Kaluza-Klein reduction on $S^2$. This provides an alternate path to the 'high-temperature' limit of the index, and confirms the connection to the right-moving central charge of the $\mathcal{N}=(0,2)$ theory.

29 pages, 1 figure; v2: restricted to real chemical potentials in section 4 and added a comment on the index where $c_r({\mathfrak{n}}_a)<0$ in section 5

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Cited by in corpus (27)

• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Lectures on AdS Black Holes, Holography and Localization
• Topologically twisted indices in five dimensions and holography
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Supersymmetric phases of 4d N=4 SYM at large N
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• Superconformal indices at large $N$ and the entropy of AdS${}_5$ $\times$ SE${}_5$ black holes
• Delayed Deconfinement and the Hawking-Page Transition
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• Black hole entropy function for toric theories via Bethe Ansatz
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• 6D attractors and black hole microstates
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• Black hole microstate counting in Type IIB from 5d SCFTs
• Superconformal index of low-rank gauge theories via the Bethe Ansatz
• Microstates of rotating AdS${}_5$ strings
• Exact QFT duals of AdS black holes
• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• The large-$N$ limit of 4d superconformal indices for general BPS charges
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• Thermodynamics of Near BPS Black Holes in AdS${}_4$ and AdS${}_7$
• New supersymmetric $Ad{S}_5$ black strings from 5D $N=4$ gauged supergravity
• Kerr-Newman black holes from $\mathcal{N}=1^{\ast }$
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail