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Invariance under reflecting temperature to negative values

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If you have a question about this talk, please contact Dr. Piotr Tourkine.

Partition functions’ convergence e.g. in statistical mechanics seem deeply tied to temperature’s positivity. Surprisingly, one can explicitly check that model partition functions—e.g. the simple harmonic oscillator, all Virasoro minimal model characters—are invariant under reflecting temperatures to negative values (T-reflection), up to an overall phase. Demanding this invariance, modulo this phase, selects a unique vacuum energy for a system. Finite temperatures in relativistic quantum field theory (QFT) are introduced through putting the theory on a circle of radius 1/T. T-reflection is related to a generic redundancy associated with the geometry of the thermal circle, and to global gravitational anomalies. Further, it had led to 2d/4d correspondences in QFT , and new conjectures in number theory.

This talk is part of the Quantum Fields and Strings Seminars series.

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