For targets
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topological AdS7/CFT6-sector
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What is called the A-model topological string is the 2-dimensional topological conformal field theory corresponding to the Calabi?Yau category called the Fukaya category of a symplectic manifold $(X,\omega)$. This is the Poisson sigma-model of the underlying Poisson manifold after appropriate gauge fixing (AKSZ 97, p 19). The A-model on $X$ is effectively the Gromov?Witten theory? of $X$.
The A-model arose in formal physics from considerations of superstring-propagation on Calabi-Yau spaces: it may be motivated by considering the vertex operator algebra of the 2dSCFT given by the supersymmetric sigma-model with target space $X$ and then deforming it such that one of the super-Virasoro generators squares to $0$. The resulting “topologically twisted” algebra may then be read as being the BRST complex of a TCFT.
One can also define an A-model for Landau?Ginzburg models. The category of D-branes for the corresponding open string theory is given by the Fukaya?Seidel category?.
By homological mirror symmetry, the A-model is dual to the B-model.
The action functional of the A-model is that associated by AKSZ theory to a Lagrangian submanifold in a target symplectic Lie n-algebroid which is the Poisson Lie algebroid of a symplectic manifold.
See the references on Lagrangian formulation.
On coisotropic branes in symplectic target manifolds that arise by complexification of phase spaces, the boundary path integral of the A-model computes the quantization of that phase space. For details see
and
The second quantization effective background field theory defined by the perturbation series of the A-model string has been argued to be Chern-Simons theory. (Witten 92, Costello 06)
For more on this see at TCFT – Worldsheet and effective background theories. A related mechanism is that of world sheets for world sheets.
induced via
perspective via | perspective |
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/ | |
$\;\;\;\;\downarrow$ on $S^4$ | compactificationon followed by |
$\;\;\;\;\downarrow$ topological sector | |
$\;\;\;\;\downarrow$ | |
on the with | worldvolume theory |
$\;\;\;\; \downarrow$ on | on / |
with invariance; | worldvolume theory with type IIB |
$\;\;\;\;\; \downarrow$ | |
$\;\;\;\; \downarrow$ on | |
on $Bun_G$, |
$\,$
induced via |
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$\;\;\;\;\downarrow$ on $S^5$ |
$\;\;\;\; \downarrow$ topological sector |
$\;\;\;\;\downarrow$ |
$\;\;\;\;\; \downarrow$ |
$\;\;\;\; \downarrow$ on |
on $Bun_G$ and on $Loc_G$, |
The A-model was first conceived in
An early review is in
The motivation from the point of view of string theory is reviewed for instance in
A summary of these two reviews is in
That the A-model Lagrangian arises in AKSZ theory by gauge fixing the Poisson sigma-model was observed in
with more details in
Review and further discussion includes
Also
Discussion of how the second quantization effective field theory given by the A-model perturbation series is Chern-Simons theory is in
formalizing at least aspects of the observations in
Last revised on July 13, 2016 at 05:01:39. See the history of this page for a list of all contributions to it.