Super Weyl invariance: BPS equations from heterotic worldsheets

113

223

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 Kähler-Hodge and we further argue that it has vanishing Kähler 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 Kähler 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.

“…We can either use the full nonlinear supergravity (see e.g. [58]), or simply use linearized supergravity as in [57] and Appendix C to show that the local counterterm is…”

Section: (02) Supersymmetric Theoriesmentioning

confidence: 99%

Anomalies, conformal manifolds, and spheres

Gomis

Hsin

Komargodski

et al. 2016

113

223

“…coincides with that of [16], and its vanishing clearly implies the spacetime gaugino equation (2.12). Our β…”

Section: Beta Functionals Of the (02) Nlsmmentioning

confidence: 77%

“…The one-loop beta functionals for (0, 2) NLSMs were derived in [16] by demanding (0, 2) super-Weyl invariance of the quantum effective action. Crucially, they found three beta functions for the theory, which are in 1-1 correspondence with the spacetime BPS equations of the heterotic string:…”

Section: Beta Functionals Of the (02) Nlsmmentioning

confidence: 99%

“…Let us write β (1) for the one-loop contribution to the beta functionals and ∆β for the sum of all higher loop contributions: β = β (1) + ∆β. 9 We will compare our approach to [16] further in what follows. For our starting point, we will take the one-loop NLSM beta functionals to be given by…”

Section: Beta Functionals Of the (02) Nlsmmentioning

confidence: 99%

“…K is a little more subtle, because it corresponds to a linear combination of the two remaining beta functionals of [16]. 10 One member of that pair reads…”

Section: Beta Functionals Of the (02) Nlsmmentioning

confidence: 99%

See 2 more Smart Citations

Conformal invariance of (0, 2) sigma models on Calabi-Yau manifolds

Jardine

Quigley

2018

GLSMs for non-Kähler geometries

Adams

Dyer

Lee

2013

We identify a simple mechanism by which H-flux satisfying the modified Bianchi identity arises in garden-variety (0, 2) gauged linear sigma models. Taking suitable limits leads to effective gauged linear sigma models with Green-Schwarz anomaly cancellation. We test the quantumconsistency of a class of such effective theories by constructing an off-shell superconformal algebra, identifying unexpected topological constraints on the existence of this algebra and providing evidence that these models run to good CFTs in the deep IR when all of the constraints are satisfied.1 The term "balanced" is probably more appropriate [2], since all such 4d N = 1 compactifications come from balanced manifolds which may or may not be Kähler. The term "non-Kähler" has become standard, however, emphasizing that these manifolds need not be Kähler.2 For useful introductions and reviews of (0,2) sigma models see [10,11].5 Note that adding a GS term is not possible in a (2, 2) model. Corespondingly, the fermionic spectrum is necessarily non-chiral, which forbids any gauge anomaly. Such models necessarily have dH = 0.6 Technically, this result uses the natural Kähler structure on the toric variety. In the presence of torsion, the physical metric will in general not be this Kähler metric. They will differ, however, only by terms proportional to α ′ , the loop counting parameter in the worldsheet; for the Bianchi identity above, we need only the leading order result. Note that this argument is not reliable away from large radius -however, away from large radius, the geometric picture is itself not reliable so we should focus instead on the quantum consistency of the gauge theory.