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.

21 pages, typos corrected

References in corpus (2)

• Interface Yang-Mills, Supersymmetry, and Janus
• Ground States of S-duality Twisted N=4 Super Yang-Mills Theory

Cited by in corpus (3)

• Trisecting non-Lagrangian theories
• Variations on S-fold CFTs
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs