DEPARTMENT OF PHYSICS DISSERTATION DEFENSE: Dan Stefan Eniceicu

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Title: Advances in Non-Perturbative String Theory

Abstract:  String theory is traditionally formulated perturbatively as the result of applying the principles of quantization to the study of two-dimensional gravity. Subsequently, calculations of quantities of interest such as correlators in the resulting theory usually involve sums which include contributions from surfaces of different topologies. In general, these sums are not convergent but correctly capture the asymptotic behavior of the quantities of interest in the weak-coupling limit. In order to go beyond asymptotic analysis and obtain exact answers, it is usually necessary to supplement these perturbative calculations with contributions from non-perturbative effects called D-brane instantons and to apply a suitable resummation technique to the resulting collection of perturbative data. However, for a certain class of string theories, one can avoid perturbation theory entirely and perform exact calculations by exploiting the duality of these string theories to the double-scaling limit of a family of unitary matrix integrals. This thesis presents evidence for the extension of the string theory/matrix integral duality beyond perturbation theory and uses the duality to derive a convergent analytic expression for the partition function of $\mathcal{N}=1$ $(2,4k)$ minimal superstring theory with type 0B GSO projection in the ungapped phase. Taking the $k\rightarrow\infty$ limit, the non-perturbatively complete partition function of $\mathcal{N}=1$ JT supergravity is also obtained. As a result, the fundamental objects of the string theory are identified as a linear combination of the standard FZZT branes of Liouville theory called F-branes, along with their charge-conjugate partners called anti-F-branes. Summing over the disk and cylinder diagram contributions of the F-branes and anti-F-branes and integrating over their moduli space reproduces the expression for the partition function derived from the matrix integral side of the duality exactly.