The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT rather than a CFT, with a UV cutoff. In the first part of the talk, I will explain Tseytlin’s prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and α′. I will also show how Tseytlin's prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with "n" operator insertions. In the second part of the talk, I will explain the underlying conceptual structure of the Susskind and Uglum black hole entropy argument. There I will show how the classical (tree-level) effective action and entropy S = A/4G_N can be calculated from the sphere diagrams. Time permitting, I will also discuss ongoing work for deriving the holographic entanglement entropy (the RT formula) in AdS3/CFT2. I will end with mentioning some important insights into how the ER=EPR hypothesis can be implemented using tachyon condensation on orbifolds in string theory.

The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT rather than a CFT, with a UV cutoff. In this talk, I will explain Tseytlin's prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and $\alpha'$. I will also show how Tseytlin's prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with "n" operator insertions. I will also explain how Tseytlin's prescriptions encode the correct prescription for the Lorentzian S-matrix in which case we obtain Feynman's $i\varepsilon$ prescription for the internal poles. Finally, I will explain how the classical off-shell string action was used by Susskind and Uglum to calculate the tree-level black hole entropy on a conical manifold in Rindler background. Time permitting, I will present very recent upcoming work on a closed-form expression for a generalized Tseytlin (GT) operator that eliminates all spurious tadpoles from higher curvature couplings on the worldsheet. This allows us to study its action on correlations functions of scalar primaries and descendants with arbitrary conformal dimensions.