SL(2, ℤ) action on QFTs with ℤ2 symmetry and the Brown-Kervaire invariants
Lakshya Bhardwaj, Yasunori Lee, Yuji Tachikawa
Abstract
A bstract We consider an analogue of Witten’s SL(2 , ℤ) action on three-dimensional QFTs with U(1) symmetry for 2 k -dimensional QFTs with ℤ 2 ( k − 1)-form symmetry. We show that the SL(2 , ℤ) action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the SL(2 , ℤ) anomaly of the bulk (2 k + 1)-dimensional ℤ 2 gauge theory.
Topics & Concepts
PhysicsAction (physics)Partition function (quantum field theory)SpacetimeInvariant (physics)Invertible matrixMathematical physicsSymmetry (geometry)Theoretical physicsAnomaly (physics)Function (biology)Symmetry groupSymmetry breakingGlobal symmetrySpace timeEffective actionSpace (punctuation)Phase spaceQuantum mechanicsBlack Holes and Theoretical PhysicsHomotopy and Cohomology in Algebraic TopologyAlgebraic structures and combinatorial models