Anomaly equations and intersection theory

By D. S. Park. 2011

137 citations recorded by the source corpus.

A bstractSix-dimensional supergravity theories with $ \mathcal{N} $ = (1, 0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional $ \mathcal{N} $ = (1, 0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric counterpart of the anomaly coefficients — in particular, those of the abelian gauge groups — that govern the low-energy dynamics of the theory. We discuss the results in the context of investigating string universality in six dimensions.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/590d586dbbe6e430936862954efb042788684ea7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

Citations in the corpus

Anomaly cancellation and abelian gauge symmetries in F-theory (2012, methodology): “It is was noted in [41, 23, 42] that it is necessary in the reduction of Mtheory on X̂4 to shift the 3D M-theory fields for the correct identification by the duality (19) with 4D F-theory fields obtained by the reduction on a circle to 3D.”
F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds (2012, methodology): “A more thorough description of the process of extracting the physical data of six-dimensional F-theory backgrounds can be found in [15, 47].”
A stringy test of the Scalar Weak Gravity Conjecture (2018, unknown): “Here [79] Cab = −π∗(σ (Sa) · σ(Sb)) (3.”
F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections (2013, background): “Anomaly cancellation in six-dimensional F-theory vacua, based on general results on 6d anomaly cancellation [59, 60], has been discussed in [55, 43], whose notations and conventions we follow here.”
Geometric engineering in toric F-theory and GUTs with U(1) gauge factors (2013, background): “Studying global U(1) symmetries is a topic of intense current research [11, 12, 13, 14, 15, 16, 17, 18, 19].”
F-theory on all toric hypersurface fibrations and its Higgs branches (2014, methodology): “5) [34], we obtain σZ2(ŝ (2) 0 ) = S (2) 0 + [K −1 B ]− S9 .”
Classifying bases for 6D F-theory models (2012, background): “U(1) factors add significant subtleties to analysis from the supergravity point of view, as discussed in [11, 12].”