IAS Physics Group Meeting

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Abstract: 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 on the worldsheet.

While Tseytlin's off-shell formalism can be used at arbitrary genus g, the treatment of the sphere diagram (genus-0) is particularly subtle. In particular, on the sphere, Tseytlin does not deal with the SL(2,C) group by fixing 3 points, as this prescription does not properly extend to the off-shell case. 

In this talk, I will explain Tseytlin’s formalism for constructing classical off-shell effective actions and provide a general proof 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. 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.