Analytic continuation of marginal couplings produces complex CFTs, with no genuinely complex rational CFTs existing, and exact defect results verified in non-Hermitian Ising and fermion chains.
Anomalies, Conformal Manifolds, and Spheres
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space M is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail N=(2,2) and N=(0,2) supersymmetric theories in d=2 and N=2 supersymmetric theories in d=4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kahler-Hodge and we further argue that it has vanishing Kahler class. For N=(2,2) theories in d=2 and N=2 theories in d=4 we also show that the relation between the sphere partition function and the Kahler potential of M follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.
citation-role summary
background 2
citation-polarity summary
fields
hep-th 3years
2026 3verdicts
UNVERDICTED 3roles
background 2representative citing papers
A 2-form connection is defined in the space of open string field theory solutions, producing invariant higher holonomies and 3-form curvature potentially corresponding to the B-field.
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
citing papers explorer
-
Complex Conformal Manifolds
Analytic continuation of marginal couplings produces complex CFTs, with no genuinely complex rational CFTs existing, and exact defect results verified in non-Hermitian Ising and fermion chains.
-
Higher Connection in Open String Field Theory
A 2-form connection is defined in the space of open string field theory solutions, producing invariant higher holonomies and 3-form curvature potentially corresponding to the B-field.
-
Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.