Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums
arXiv:1912.11471 · doi:10.1007/JHEP05(2021)227
Abstract
We study the supersymmetric partition function of a 2d linear -model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d Super-Yang-Mills theory compactified on a mapping torus ( fibered over ) times a circle with an duality wall inserted on , but our setup has minimal supersymmetry. The partition function depends on two independent elements of , one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the {\it Landsberg-Schaar} relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.
arXiv comment66pp; Appendix C.2-C.4 enriched, hyperlinks fixed, refs updated
References in corpus (43)
- Supersymmetry and Quantum Mechanics
- Evidence for F-Theory
- N=2 dualities
- Target Space Duality in String Theory
- S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
- Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
- Fermion Path Integrals And Topological Phases
- A Dilatonic Deformation of AdS_5 and its Field Theory Dual
- Duality Twists, Orbifolds, and Fluxes
- Geometric Constructions of Nongeometric String Theories
- Generalised T-Duality and Non-Geometric Backgrounds
- The Virtue of Defects in 4D Gauge Theories and 2D CFTs
- SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
- Surface Operators in N=2 4d Gauge Theories
- Fivebranes and 3-manifold homology
- Interface Yang-Mills, Supersymmetry, and Janus
- A Note On Zeroes Of Superpotentials In F-Theory
- Super Janus
- Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
- String Islands
- 3d Modularity
- Holographic duals of 3d S-fold CFTs
- S-Duality in Gauge Theories as a Canonical Transformation
- Anomaly of the Electromagnetic Duality of Maxwell Theory
- Topological duality twist and brane instantons in F-theory
- Aspects of Defects in 3d-3d Correspondence
- Abelian duality, walls and boundary conditions in diverse dimensions
- Janus and Multifaced Supersymmetric Theories
- Janus and Multifaced Supersymmetric Theories II
- 3d-3d correspondence for mapping tori
- A study of time reversal symmetry of abelian anyons
- U-duality Twists and Possible Phase Transitions in 2+1D Supergravity
- Janus configurations with SL(2,Z)-duality twists, Strings on Mapping Tori, and a Tridiagonal Determinant Formula
- On classification of extremal non-holomorphic conformal field theories
- Congruence Subgroups and Super-Modular Categories
- Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
- Taming Supersymmetric Defects in 3d-3d Correspondence
- Gauss Sums and Quantum Mechanics
- Janus interface in two-dimensional supersymmetric gauge theories
- Ground States of Duality-twisted Sigma-Models with K3 Target Space
- Symplectic Quantum Mechanics and Chern-Simons Gauge Theory II: Mapping Tori of Tori
- On Quadratic Gauss Sums and Variations Thereof
- Gauge theories on spheres with 16 supercharges and non-constant couplings