Janus configurations with SL(2,Z)-duality twists, Strings on Mapping Tori, and a Tridiagonal Determinant Formula

Abstract

We develop an equivalence between two Hilbert spaces: (i) the space of states of $U(1{)}^n$ Chern-Simons theory with a certain class of tridiagonal matrices of coupling constants (with corners) on $T^2$; and (ii) the space of ground states of strings on an associated mapping torus with $T^2$ fiber. The equivalence is deduced by studying the space of ground states of $SL(2,Z)$-twisted circle compactifications of $U(1)$ gauge theory, connected with a Janus configuration, and further compactified on $T^2$. The equality of dimensions of the two Hilbert spaces (i) and (ii) is equivalent to a known identity on determinants of tridiagonal matrices with corners. The equivalence of operator algebras acting on the two Hilbert spaces follows from a relation between the Smith normal form of the Chern-Simons coupling constant matrix and the isometry group of the mapping torus, as well as the torsion part of its first homology group.

arXiv comment21 pages, typos corrected

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Cited by in corpus (14)

• Type II origin of dyonic gaugings
• Holographic duals of 3d S-fold CFTs
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• Holographic Interfaces in N=4 SYM: Janus and J-folds
• Janus and J-fold Solutions from Sasaki-Einstein Manifolds
• Supersymmetric Indices of 3d S-fold SCFTs
• Trisecting non-Lagrangian theories
• The moduli spaces of S-fold CFTs
• Universal relations for holographic interfaces
• Variations on S-fold CFTs
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• T-duality Twists and Asymmetric Orbifolds
• Marginal deformations and RG flows for type IIB S-folds
• Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums