Odd Dimensional Nonlocal Liouville Conformal Field Theories

Abstract

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a $\mathcal{Q}$-curvature background, and an exponential Liouville-type potential. We study the classical and quantum properties of these theories including the finite entanglement entropy part of the sphere partition function $F$, the boundary conformal anomaly and vertex operators' correlation functions. We derive the analogue of the even-dimensional DOZZ formula and its semi-classical approximation.

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Cited by in corpus (2)

• Boundaries in Free Higher Derivative Conformal Field Theories
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