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Universal Constraints On 2d Cfts And 3d Gravity, Joshua D. Qualls

Theses and Dissertations--Physics and Astronomy

We study constraints imposed on a general unitary two-dimensional conformal field theory by modular invariance. We begin with a review of previous bounds on the conformal dimension Delta₁ of the lowest primary operator assuming unitarity, a discrete spectrum, modular invariance, c_L, c_R > 1, and no extended chiral algebra. We then obtain bounds on the conformal dimensions Delta₂, Delta₃ using no additional assumptions. We also show that in order to find a bound for Delta₄ or higher Delta_n, we need to assume a larger minimum value for c_tot that grows …