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## Main Question or Discussion Point

Take a cylindrical worldsheet parametrized by σ

The Hilbert space of states in string theory is defined by functions on the circular boundaries φ(σ

φ(σ

where e

τ = β + iθ

where θ is the range of σ

tr q

where q = e

τ → (aτ + b)/(cτ + d)

are important. The lagrangian for the CFT is of the form

L = √g g

where dx

Here account must be taken of kappa symmetry. The various CFTs obtained in this way form a web, which only in certain limiting regions of this web take the form of recognizable CFTs, like the type IIA, type IIB, etc. Open string theory in a sense has super Yang-Mills theory as its low energy limit. What are some current proposals about how to describe this web of CFTs?

^{1}and σ^{2}. The first goes along the length of the cylinder, and the other along its circumference.The Hilbert space of states in string theory is defined by functions on the circular boundaries φ(σ

^{1}) and the evolution of this state along the cylinder is given byφ(σ

^{1}) → e^{-βH}φ(σ^{1})where e

^{-βH}is the density operator of thermodynamics. These circular boundaries can be mapped to a puncture using conformal transformations, and states in the Hilbert space correspond to operator insertion at the location of the puncture. If we defineτ = β + iθ

where θ is the range of σ

^{1}, then the partition function istr q

^{p+}q^{p-}where q = e

^{2πiτ}. The transformations of τ of the formτ → (aτ + b)/(cτ + d)

are important. The lagrangian for the CFT is of the form

L = √g g

_{ij}dx^{i}∧ *dx^{j}where dx

^{i}→ dx^{i}+ iσ^{a}θ_{a}dθ^{i}Here account must be taken of kappa symmetry. The various CFTs obtained in this way form a web, which only in certain limiting regions of this web take the form of recognizable CFTs, like the type IIA, type IIB, etc. Open string theory in a sense has super Yang-Mills theory as its low energy limit. What are some current proposals about how to describe this web of CFTs?

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