On Higher Topological T-duality Functors
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912741383471104 |
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| author | Pande, Ashwin S. |
| author_facet | Pande, Ashwin S. |
| contents | We use String Field Theory (SFT) to construct a higher analogue of Bunke-Schick's functor $P: \mathbf{Top}^{op} \to \mathbf{Set}$ \cite{BunkeS1} by geometrizing $P.$ We use the projection of SFT onto its massless modes \cite{SFTDiffeo} to construct the category $\C$ whose objects are pairs (which we identify with SFT backgrounds) and whose maps are morphisms of pairs (which are gauge transformations). Using $\C$ and categorical equivalence, for any $CW-$complex $X$ we define the moduli space $G(X)$ of SFT backgrounds which are pairs over $X$ up to gauge equivalence. We use the homotopy theory of the moduli space $G(X)$ to define functors on the category of $CW-$complexes $P_k:\mathbf{CW}^{op} \to \mathbf{Grpd}$ such that $P_0 \simeq P,$ $P_1$ is nontrivial and $P_k(X)$ are always trivial for $k \geq 2.$ Arrows in $P_1(X)$ are shown to be isotopy classes of maps in the mapping class group of $X$ acting on (isomorphism classes of) pairs over $X.$ We discuss applications to Topological T-duality for triples and to modelling doubled geometries and T-folds \cite{HullT}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Higher Topological T-duality Functors Pande, Ashwin S. Mathematical Physics High Energy Physics - Theory Algebraic Topology 81T30, 83E30, 55Q05, 55Q70, 18N50, 55U10 We use String Field Theory (SFT) to construct a higher analogue of Bunke-Schick's functor $P: \mathbf{Top}^{op} \to \mathbf{Set}$ \cite{BunkeS1} by geometrizing $P.$ We use the projection of SFT onto its massless modes \cite{SFTDiffeo} to construct the category $\C$ whose objects are pairs (which we identify with SFT backgrounds) and whose maps are morphisms of pairs (which are gauge transformations). Using $\C$ and categorical equivalence, for any $CW-$complex $X$ we define the moduli space $G(X)$ of SFT backgrounds which are pairs over $X$ up to gauge equivalence. We use the homotopy theory of the moduli space $G(X)$ to define functors on the category of $CW-$complexes $P_k:\mathbf{CW}^{op} \to \mathbf{Grpd}$ such that $P_0 \simeq P,$ $P_1$ is nontrivial and $P_k(X)$ are always trivial for $k \geq 2.$ Arrows in $P_1(X)$ are shown to be isotopy classes of maps in the mapping class group of $X$ acting on (isomorphism classes of) pairs over $X.$ We discuss applications to Topological T-duality for triples and to modelling doubled geometries and T-folds \cite{HullT}. |
| title | On Higher Topological T-duality Functors |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Topology 81T30, 83E30, 55Q05, 55Q70, 18N50, 55U10 |
| url | https://arxiv.org/abs/2402.12039 |