The Verlinde formula for Higgs bundles

Abstract

We propose and prove the Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. This generalizes the equivariant Verlinde formula for the case of $SU(n)$ proposed previously by the second and third author. We further establish a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. Finally, we prove that these dimensions form a one-parameter family of $1+1$-dimensional TQFT, uniquely classified by the complex Verlinde algebra, which is a one-parameter family of Frobenius algebras. We construct this one-parameter family of Frobenius algebras as a deformation of the classical Verlinde algebra for $G$.

39 pages; references added, misprints corrected and exposition improved

References in corpus (2)

• Complex Quantum Chern-Simons
• The equivariant Verlinde formula on the moduli of Higgs bundles

Cited by in corpus (2)

• Mirror symmetry with branes by equivariant Verlinde formulae
• Level N Teichmüller TQFT and Complex Chern-Simons Theory