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Weyl invariance, non-compact duality and conformal higher-derivative sigma models | | Darren T. Grasso
; Sergei M. Kuzenko
; Joshua R. Pinelli
; | | Date: |
2 Jan 2023 | | Abstract: | We study a system of $n$ Abelian vector fields coupled to $frac 12 n(n+1)$
complex scalars parametrising the Hermitian symmetric space $mathsf{Sp}(2n,
{mathbb R})/ mathsf{U}(n)$. This model is Weyl invariant and possesses the
maximal non-compact duality group $mathsf{Sp}(2n, {mathbb R})$. Although both
symmetries are anomalous in the quantum theory, they should be respected by the
logarithmic divergent term (the ’’induced action’’) of the effective action
obtained by integrating out the vector fields. We compute this induced action
and demonstrate its Weyl and $mathsf{Sp}(2n, {mathbb R})$ invariance. The
resulting conformal higher-derivative $sigma$-model on $mathsf{Sp}(2n,
{mathbb R})/ mathsf{U}(n)$ is generalised to the cases where the fields take
their values in (i) an arbitrary Kähler space; and (ii) an arbitrary
Riemannian manifold. In both cases, the $sigma$-model Lagrangian generates a
Weyl anomaly satisfying the Wess-Zumino consistency condition. | | Source: | arXiv, 2301.00577 | | Services: | Forum | Review | PDF | Favorites | |
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