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- W4361193003 abstract "The partition functions of free bosons as well as fermions on $AdS_2$ are not smooth as a function of their masses. For free bosons, the partition function on $AdS_2$ is not smooth when the mass saturates the Breitenlohner-Freedman bound. We show that the expectation value of the scalar bilinear on $AdS_2$ exhibits a kink at the BF bound and the change in slope of the expectation value with respect to the mass is proportional to the inverse radius of $AdS_2$. For free fermions, when the mass vanishes the partition function exhibits a kink. We show that expectation value of the fermion bilinear is discontinuous and the jump in the expectation value is proportional to the inverse radius of $AdS_2$. We then show the supersymmetric actions of the chiral multiplet on $AdS_2times S^1$ and the hypermultiplet on $AdS_2times S^2$ demonstrate these features. The supersymmetric backgrounds are such that as the ratio of the radius of $AdS_2$ to $S^1$ or $S^2$ is dialled, the partition functions as well as expectation of bilinears are not smooth for each Kaluza-Klein mode on $S^1$ or $S^2$. Our observation is relevant for evaluating one-loop partition function in the near horizon geometry of extremal black holes." @default.
- W4361193003 created "2023-03-31" @default.
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- W4361193003 date "2023-03-25" @default.
- W4361193003 modified "2023-09-25" @default.
- W4361193003 title "Discontinuities of free theories on $AdS_2$" @default.
- W4361193003 doi "https://doi.org/10.48550/arxiv.2303.14354" @default.
- W4361193003 hasPublicationYear "2023" @default.
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